You can try the following approach::
d = re.split(r"([a-zA-Z]+\,\s+[a-zA-Z]+)", d)[1:]
d = [", ".join(d[i:i+2]) for i in range(0, len(d), 2)]
d = [re.findall(r'^(.*?)\s+\((.*?)\)\s+(.*?\d{4})(.*?)$', _)[0] for _ in d]
df = pd.DataFrame(d, columns=["name", "party/state", "date_to_convert", "rank_to_clean"])
df["name"] = df["name"].str.replace(r'\,$','')
Workflow:
- Split the input on - ,surrounded by two Names:
 - 
- Use the regex [a-zA-Z]+\,\s+[a-zA-Z]+
- Surround the regex by parenthesis because the split key (e.g. the names) need to be kept
- Apply regex using re.split
- Remove first element that is empty space
 
- Here, we have all the lines bu divided in two elements. We need to aggregate two consecutive element. The topic Create a 2D list out of 1D list answer this step.  
- Now content can be extracted from each row. Here, we use - re.findallwith regex- (.*?)\s+\((.*?)\)\s+(.*?\d{4})(.*?)$. They are 4 groups:
 - 
- Group 1 selects everything till a parenthesis: (.*?)\s+\(
- Group 2 selects everything till the closing parenthesis: (.*?)\)
- Group 3 selects everything till a year (e.g. 4 numbers): (.*?\d{4})
- Group 4 selects everything till the end: (.*?)$
 
For a better understanding of regex, I advice you to see online regex such as regex101.com to visualize the results...
- Create the dataframe
Next steps, apply more specific cleanings and separation on dataset such as removing comma on name with:
df["name"] = df["name"].str.replace(r'\,$','')
Code + illustration
# import module
import pandas as pd
import re
d = "Silsbee, Nathaniel (Adams/AJ-MA) March 3, 1835  281 November 8 Rodney, Daniel (Adams-DE) January 12, 1827  282 November 9 Bateman, Ephraim (Adams-NJ) January 12, 1829  283 November 27 McKinley, John (J-AL) March 3, 1831  284   (Served again 1837) November 29 Smith, William (R-SC) March 3, 1831   (First served 1816-1823)  * * * 1827 * * * January 12 Ridgely, Henry M. (J-DE) March 3, 1829  285   TWENTIETH CONGRESS March 4, 1827, TO MARCH 3, 1829  March 4 Barnard, Isaac D. (J-PA) December 6, 1831  286  Ellis, Powhatan (J-MS) July 16, 1832   (First served 1825-1826)  Foot, Samuel A. (Adams/AJ-CT) March 3, 1833  287  McLane, Louis (J-DE) April 16, 1829  288  Parris, Albion K. (J-ME) August 26, 1828  289  Tyler, John (J/AJ-VA) February 29, 1836  290 December 17 Webster, Daniel (Adams/AJ/W-MA) February 22, 1841  291   (Served again 1845)  * * * 1828 * * * November 7 Prince, Oliver H. (J-GA) March 3, 1829  292 Start of Initial    Senate Service Name/Party   End of Service Rank    15 December 10 Burnet, Jacob (Adams/AJ-OH) March 3, 1831  293 December 15 Iredell, James (J-NC) March 3, 1831  294  * * * 1829 * * * January 15 Dudley, Charles E. (J-NY) March 3, 1833  295  Holmes, John (Adams/AJ-ME) March 3, 1833   (First served 1820-1827) January 30 Dickerson, Mahlon (R/CR/J-NJ) March 3, 1833   (First served 1817-1829)"
# Step 1
d = re.split(r"([a-zA-Z]+\,\s+[a-zA-Z]+)", d)[1:]
print(d)
# ['Silsbee, Nathaniel', ' (Adams/AJ-MA) March 3, 1835  281 November 8 ',
#  'Rodney, Daniel', ' (Adams-DE) January 12, 1827  282 November 9 ', 
#  'Bateman, Ephraim', ' (Adams-NJ) January 12, 1829  283 November 27 ', 
#  'McKinley, John', ' (J-AL) March 3, 1831  284   (Served again 1837) November 29 ', 
#  'Smith, William', ' (R-SC) March 3, 1831   (First served 1816-1823)  * * * 1827 * * * January 12 ',
#  'Ridgely, Henry', ' M. (J-DE) March 3, 1829  285   TWENTIETH CONGRESS March 4, 1827, TO MARCH 3, 1829  March 4 ',
#  'Barnard, Isaac', ' D. (J-PA) December 6, 1831  286  ',
#  'Ellis, Powhatan', ' (J-MS) July 16, 1832   (First served 1825-1826)  ',
#  'Foot, Samuel', ' A. (Adams/AJ-CT) March 3, 1833  287  ',
#  'McLane, Louis', ' (J-DE) April 16, 1829  288  ',
#  'Parris, Albion', ' K. (J-ME) August 26, 1828  289  ',
#  'Tyler, John', ' (J/AJ-VA) February 29, 1836  290 December 17 ',
#  'Webster, Daniel', ' (Adams/AJ/W-MA) February 22, 1841  291   (Served again 1845)  * * * 1828 * * * November 7 ',
#  'Prince, Oliver', ' H. (J-GA) March 3, 1829  292 Start of Initial    Senate Service Name/Party   End of Service Rank    15 December 10 ',
#  'Burnet, Jacob', ' (Adams/AJ-OH) March 3, 1831  293 December 15 ',
#  'Iredell, James', ' (J-NC) March 3, 1831  294  * * * 1829 * * * January 15 ',
#  'Dudley, Charles', ' E. (J-NY) March 3, 1833  295  ',
#  'Holmes, John', ' (Adams/AJ-ME) March 3, 1833   (First served 1820-1827) January 30 ',
#  'Dickerson, Mahlon', ' (R/CR/J-NJ) March 3, 1833   (First served 1817-1829)']
# Step 2
d = [", ".join(d[i:i+2]) for i in range(0, len(d), 2)]
print(d)
# ['Silsbee, Nathaniel,  (Adams/AJ-MA) March 3, 1835  281 November 8 ',
#  'Rodney, Daniel,  (Adams-DE) January 12, 1827  282 November 9 ',
#  'Bateman, Ephraim,  (Adams-NJ) January 12, 1829  283 November 27 ',
#  'McKinley, John,  (J-AL) March 3, 1831  284   (Served again 1837) November 29 ',
#  'Smith, William,  (R-SC) March 3, 1831   (First served 1816-1823)  * * * 1827 * * * January 12 ',
#  'Ridgely, Henry,  M. (J-DE) March 3, 1829  285   TWENTIETH CONGRESS March 4, 1827, TO MARCH 3, 1829  March 4 ',
#  'Barnard, Isaac,  D. (J-PA) December 6, 1831  286  ',
#  'Ellis, Powhatan,  (J-MS) July 16, 1832   (First served 1825-1826)  ',
#  'Foot, Samuel,  A. (Adams/AJ-CT) March 3, 1833  287  ', 'McLane, Louis,  (J-DE) April 16, 1829  288  ',
#  'Parris, Albion,  K. (J-ME) August 26, 1828  289  ',
#  'Tyler, John,  (J/AJ-VA) February 29, 1836  290 December 17 ',
#  'Webster, Daniel,  (Adams/AJ/W-MA) February 22, 1841  291   (Served again 1845)  * * * 1828 * * * November 7 ',
#  'Prince, Oliver,  H. (J-GA) March 3, 1829  292 Start of Initial    Senate Service Name/Party   End of Service Rank    15 December 10 ',
#  'Burnet, Jacob,  (Adams/AJ-OH) March 3, 1831  293 December 15 ',
#  'Iredell, James,  (J-NC) March 3, 1831  294  * * * 1829 * * * January 15 ',
#  'Dudley, Charles,  E. (J-NY) March 3, 1833  295  ',
#  'Holmes, John,  (Adams/AJ-ME) March 3, 1833   (First served 1820-1827) January 30 ',
#  'Dickerson, Mahlon,  (R/CR/J-NJ) March 3, 1833   (First served 1817-1829)']
# Step 3
d = [re.findall(r'^(.*?)\s+\((.*?)\)\s+(.*?\d{4})(.*?)$', _)[0] for _ in d]
[print(_) for _ in d]
# ('Silsbee, Nathaniel,', 'Adams/AJ-MA', 'March 3, 1835', '  281 November 8 ')
# ('Rodney, Daniel,', 'Adams-DE', 'January 12, 1827', '  282 November 9 ')
# ('Bateman, Ephraim,', 'Adams-NJ', 'January 12, 1829', '  283 November 27 ')
# ('McKinley, John,', 'J-AL', 'March 3, 1831', '  284   (Served again 1837) November 29 ')
# ('Smith, William,', 'R-SC', 'March 3, 1831', '   (First served 1816-1823)  * * * 1827 * * * January 12 ')
# ('Ridgely, Henry,  M.', 'J-DE', 'March 3, 1829', '  285   TWENTIETH CONGRESS March 4, 1827, TO MARCH 3, 1829  March 4 ')
# ('Barnard, Isaac,  D.', 'J-PA', 'December 6, 1831', '  286  ')
# ('Ellis, Powhatan,', 'J-MS', 'July 16, 1832', '   (First served 1825-1826)  ')
# ('Foot, Samuel,  A.', 'Adams/AJ-CT', 'March 3, 1833', '  287  ')
# ('McLane, Louis,', 'J-DE', 'April 16, 1829', '  288  ')
# ('Parris, Albion,  K.', 'J-ME', 'August 26, 1828', '  289  ')
# ('Tyler, John,', 'J/AJ-VA', 'February 29, 1836', '  290 December 17 ')
# ('Webster, Daniel,', 'Adams/AJ/W-MA', 'February 22, 1841', '  291   (Served again 1845)  * * * 1828 * * * November 7 ')
# ('Prince, Oliver,  H.', 'J-GA', 'March 3, 1829', '  292 Start of Initial    Senate Service Name/Party   End of Service Rank    15 December 10 ')
# ('Burnet, Jacob,', 'Adams/AJ-OH', 'March 3, 1831', '  293 December 15 ')
# ('Iredell, James,', 'J-NC', 'March 3, 1831', '  294  * * * 1829 * * * January 15 ')
# ('Dudley, Charles,  E.', 'J-NY', 'March 3, 1833', '  295  ')
# ('Holmes, John,', 'Adams/AJ-ME', 'March 3, 1833', '   (First served 1820-1827) January 30 ')
# ('Dickerson, Mahlon,', 'R/CR/J-NJ', 'March 3, 1833', '   (First served 1817-1829)')
# Step 4
df = pd.DataFrame(d, columns=["name", "party/state", "date_to_convert", "rank_to_clean"])
df["name"] = df["name"].str.replace(r'\,$','')
print(df)
#                     name    party/state    date_to_convert                                      rank_to_clean
# 0     Silsbee, Nathaniel    Adams/AJ-MA      March 3, 1835                                    281 November 8 
# 1         Rodney, Daniel       Adams-DE   January 12, 1827                                    282 November 9 
# 2       Bateman, Ephraim       Adams-NJ   January 12, 1829                                   283 November 27 
# 3         McKinley, John           J-AL      March 3, 1831             284   (Served again 1837) November 29 
# 4         Smith, William           R-SC      March 3, 1831     (First served 1816-1823)  * * * 1827 * * * ...
# 5    Ridgely, Henry,  M.           J-DE      March 3, 1829    285   TWENTIETH CONGRESS March 4, 1827, TO M...
# 6    Barnard, Isaac,  D.           J-PA   December 6, 1831                                              286  
# 7        Ellis, Powhatan           J-MS      July 16, 1832                         (First served 1825-1826)  
# 8      Foot, Samuel,  A.    Adams/AJ-CT      March 3, 1833                                              287  
# 9          McLane, Louis           J-DE     April 16, 1829                                              288  
# 10   Parris, Albion,  K.           J-ME    August 26, 1828                                              289  
# 11           Tyler, John        J/AJ-VA  February 29, 1836                                   290 December 17 
# 12       Webster, Daniel  Adams/AJ/W-MA  February 22, 1841    291   (Served again 1845)  * * * 1828 * * * ...
# 13   Prince, Oliver,  H.           J-GA      March 3, 1829    292 Start of Initial    Senate Service Name/...
# 14         Burnet, Jacob    Adams/AJ-OH      March 3, 1831                                   293 December 15 
# 15        Iredell, James           J-NC      March 3, 1831                  294  * * * 1829 * * * January 15 
# 16  Dudley, Charles,  E.           J-NY      March 3, 1833                                              295  
# 17          Holmes, John    Adams/AJ-ME      March 3, 1833               (First served 1820-1827) January 30 
# 18     Dickerson, Mahlon      R/CR/J-NJ      March 3, 1833                           (First served 1817-1829)