Almost top before Cambridge University check (5)
I believe the answer is:
limit
'check' is the definition.
(limit can mean to check or restrain)
'almost top before cambridge university' is the wordplay.
'almost' means to remove the last letter (almost the whole word is kept).
'top' becomes 'lid' (lid is a kind of top).
'before' says to put letters next to each other.
'cambridge university' becomes 'MIT' (MIT in Cambridge, Massachusetts).
'lid' with its final letter taken away is 'li'.
'li'+'mit'='LIMIT'
(Other definitions for limit that I've seen before include "qualify?" , "Breaking point" , "Boundary or maximum" , "Outer extent" , "Furthest point" .)