Sat second exam primarily in school (5)
I believe the answer is:
posed
'sat' is the definition.
('pose' can be a synonym of 'sit')
'second exam primarily in school' is the wordplay.
'primarily' suggests taking the first letters.
'in' is an insertion indicator.
'school' becomes 'pod' (I've seen this before**).
The initial letters of 'second exam' is 'se'.
'se' going within 'pod' is 'POSED'.
(Other definitions for posed that I've seen before include "Struck attitude, perhaps for painter" , "Assumed" , "Sat (for artist)" , "Presented (a question)" , "Modelled" .)