University exercises right to be included, but it's not ready (6)
I believe the answer is:
unripe
'it's not ready' is the definition.
(not yet ready to eat)
'university exercises right to be included' is the wordplay.
'university' becomes 'uni' (short for university).
'exercises' becomes 'pe' (Physical Education class).
'right' becomes 'r' (common abbreviation).
'to be included' indicates putting letters inside.
'uni'+'pe'='unipe'
'unipe' placed around 'r' is 'UNRIPE'.
'but' is the link.
(Other definitions for unripe that I've seen before include "Immature" , "Still green?" , "Punier (anag.)" , "Not ready for picking" , "Not yet mature" .)