The most common and most likely answer to this crossword clue is the 7 letter word ALUMNUS
I've seen this crossword clue in Financial Times
A
L
U
M
N
U
S
More clues leading to the result ALUMNUS
- Former student requiring a reduction in mass student body
- Former student record disheartened their association
- Old pupil a bright one nothing escapes
- Case of slander dropped by American graduate
- Maul poor current students and one old one
- An article by American snubbing company’s old member
- Former student, advanced student, group of students? Expression of doubt creeps in
- Old boy, Greek character, entering a slum for demolition
- Foreign character in a slum disturbed old boy
- Going round university, almost all male students graduate
Buddy explains!

The straight part
We know that "graduate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case graduate = alumnus.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.
What does ALUMNUS mean?
ALUMNUS noun- A male pupil or student.
- A male graduate.
- A student of any gender.
- A graduate of any gender.