Here under the hood loops by apply are not necessary, you canvectorized solution - added parantheses because priority operator with & for bitwise AND to mask and new column is created by numpy.where:
#changed data for match first row
data2 = pd.DataFrame({'Unit of Measure' : ['EA', 'EA', 'AA'],
                     'round' : ['no', 'yes', 'no'],
                     'add_gst' : ['yes', 'yes', 'no'],
                     'Unit Charge' : [1.8, 2.5, 3.0],
                     'Time Units' : [1.0, 1.5, 2.0]})
print (data2)
  Unit of Measure round add_gst  Unit Charge  Time Units
0              EA    no     yes          1.8         1.0
1              EA   yes     yes          2.5         1.5
2              AA    no      no          3.0         2.0
  Unit of Measure round add_gst  Unit Charge  Time Units  
m = (data2['Unit of Measure'] == 'EA') & (data2['round'] == 'no') & (data2['add_gst'] == 'yes')
rounded = data2['Unit Charge'] * data2['Time Units']
rounded = rounded.round(2) # to two decimal places
rounded = rounded * 1.10 # add gst
rounded = rounded / 0.05 # round to nearest five cents - step 1 - divide by 0.05
rounded = rounded.round() # round to nearest five cents - step 2 - to nearest integer
rounded = rounded * 0.05 # round to nearest five cents - step 3 - multiply by 0.05
data2['incl_gst'] = np.where(m, rounded, 1.0)
print (data2)
  Unit of Measure round add_gst  Unit Charge  Time Units  incl_gst
0              EA    no     yes          1.8         1.0       2.0
1              EA   yes     yes          2.5         1.5       1.0
2              AA    no      no          3.0         2.0       1.0
EDIT:
Because 12 times elif statement solution should be cahnged:
def include_gst(df):
    rounded = 0.0
    if (df['Unit of Measure'] == 'EA') and (df['round'] == 'no') and (df['add_gst'] == 'yes'):
        rounded = df['Unit Charge'] * df['Time Units']
        rounded = round(rounded, 2) # to two decimal places
        rounded = rounded * 1.10 # add gst
        rounded = rounded / 0.05 # round to nearest five cents - step 1 - divide by 0.05
        rounded = round(rounded) # round to nearest five cents - step 2 - to nearest integer
        rounded = rounded * 0.05 # round to nearest five cents - step 3 - multiply by 0.05
        return  rounded
    else:
        return 1.0
data2['incl_gst'] = data2.apply(include_gst, axis = 1)
print (data2)
  Unit of Measure round add_gst  Unit Charge  Time Units  incl_gst
0              EA    no     yes          1.8         1.0       2.0
1              EA   yes     yes          2.5         1.5       1.0
2              AA    no      no          3.0         2.0       1.0
Or:
data2 = pd.DataFrame({'Unit of Measure' : ['EA', 'EA', 'AA'],
                     'round' : ['no', 'yes', 'no'],
                     'add_gst' : ['yes', 'yes', 'no'],
                     'Unit Charge' : [1.8, 2.5, 3.0],
                     'Time Units' : [1.0, 1.5, 2.0]})
print (data2)
  Unit of Measure round add_gst  Unit Charge  Time Units
0              EA    no     yes          1.8         1.0
1              EA   yes     yes          2.5         1.5
2              AA    no      no          3.0         2.0
m1 = (data2['Unit of Measure'] == 'EA') & (data2['round'] == 'no') & (data2['add_gst'] == 'yes')
m2 = (data2['Unit of Measure'] == 'EA') & (data2['round'] == 'yes') & (data2['add_gst'] == 'yes')
rounded = data2['Unit Charge'] * data2['Time Units']
rounded = rounded.round(2) # to two decimal places
rounded = rounded * 1.10 # add gst
rounded = rounded / 0.05 # round to nearest five cents - step 1 - divide by 0.05
rounded = rounded.round() # round to nearest five cents - step 2 - to nearest integer
rounded1 = rounded * 0.05 # round to nearest five cents - step 3 - multiply by 0.05
rounded2 = rounded * 0.08
data2['incl_gst'] = np.select([m1, m2], [rounded1, rounded2], default=1.0)
print (data2)
  Unit of Measure round add_gst  Unit Charge  Time Units  incl_gst
0              EA    no     yes          1.8         1.0      2.00
1              EA   yes     yes          2.5         1.5      6.56
2              AA    no      no          3.0         2.0      1.00