If you have a DATE column then it does not have any format; it is stored internally as 7-bytes (century, year-of-century, month, day, hour, minute, second) and it is only when the user interface being used to access the database returns data to the user that it then gets formatted (and all the dates will be implicitly converted to strings with a consistent format).
I'm going to assume that when you say:
I have a date field called "HIGH_DATE"
What you actually mean is: "I have a column with a VARCHAR2 data-type where I store date values".
If that is the case then all you need to do is:
SELECT TO_DATE( high_date, 'DD-MM-RR' ) AS high_date
FROM   table_name;
Oracle's string-to-date conversion rules will match additionally the MON format model if you use the MM format model and don't specify an exact match using the FX format model.
If you have the test data:
CREATE TABLE table_name ( high_date ) AS
SELECT '23-09-20' FROM DUAL UNION ALL
SELECT '15-AUG-99' FROM DUAL;
Then the above query will output (depending on your NLS_DATE_FORMAT):
| HIGH_DATE           |
| :------------------ |
| 2020-09-23T00:00:00 |
| 1999-08-15T00:00:00 |
db<>fiddle here
However, the best solution is going to be to stop storing the values as strings and to store them (without a format) as a date.