Cheerful at university, but started to worry (6)
I believe the answer is:
upbeat
'cheerful' is the definition.
('upbeat' can be a synonym of 'cheerful')
'at university but started to worry' is the wordplay.
'at university' becomes 'up'.
'started to' says to take the initial letters (I've seen 'start to' mean this).
'worry' becomes 'eat' (eating is a kind of worrying).
The first letter of 'but' is 'b'.
'up'+'b'+'eat'='UPBEAT'
(Other definitions for upbeat that I've seen before include "bright and cheery" , "Conductor's beginning" , "Cheerful and encouraging, like lively music" , "Relentlessly optimistic" , "Heartening" .)