Issue primarily engaging American university (4)
I believe the answer is:
emit
'issue' is the definition.
(both can mean to give out or radiate)
'primarily engaging american university' is the wordplay.
'primarily' indicates taking the first letters.
'american university' becomes 'MIT' (Massachusetts Institute of Technology).
The first letter of 'engaging' is 'e'.
'e'+'mit'='EMIT'
(Other definitions for emit that I've seen before include "Release" , "Come out!" , "Give off, heat say" , "Sent" , "Give off, gas say" .)