The most common and most likely answer to this crossword clue is the 4 plus 5 letter word ALMA MATER
I've seen this crossword clue in The Guardian
A
L
M
A
M
A
T
E
R
More clues leading to the result ALMA MATER
- Old lady overwhelmed by change, being old school
- Old school needs to adjust about a couple of degrees
- Old school graduates block change
- School mums involved in reform
- Two scholars put into reform school
- The old lady twice breaking into reform school she once attended?
- Old school masters block change
- Keeping mum, change college
- Graduate repeatedly brought in to reform old university
- Old school friend goes in wild alarm …
Buddy explains!

The straight part
We know that "old university" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old university = alma mater.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.