Clap a very quiet youth outside university (7)
I believe the answer is:
applaud
'clap' is the definition.
('applaud' can be a synonym of 'clap')
'a very quiet youth outside university' is the wordplay.
'very quiet' becomes 'pp'.
'youth' becomes 'lad' (I've seen this before).
'outside' indicates putting letters inside.
'university' becomes 'u'.
'lad' enclosing 'u' is 'laud'.
'a'+'pp'+'laud'='APPLAUD'
(Other definitions for applaud that I've seen before include "Cheer" , "Big up" , "Express approbation" , "Clap (a performance)" , "Approve with clapping" .)