Prompted college to replace verb in request by director (7)
I believe the answer is:
incited
'prompted' is the definition.
('incite' can be a synonym of 'prompt')
'in request by director' is the wordplay.
'request by' becomes 'cite' (I can't justify this - if you can you should believe this answer much more).
'director' becomes 'd' (abbreviation eg in film reviews).
'in'+'cite'+'d'='INCITED'
'college to replace verb' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for incited that I've seen before include "Egged on to action as in edict" , "Stirred up (unlawful activity)" , "was much encouraged" , "Pushed" , "Goaded into action" .)