Publicity given to university grant (5)
I believe the answer is:
admit
'grant' is the definition.
(I've seen this before)
'publicity given to university' is the wordplay.
'publicity' becomes 'ad' (advert).
'given to' says to put letters next to each other.
'university' becomes 'MIT' (Massachusetts Institute of Technology).
'ad'+'mit'='ADMIT'
(Other definitions for admit that I've seen before include "Confess (to something)" , "Confess - let in" , "Allow entry" , "Confess - acknowledge" , "Allow to enter; own up" .)