Rap session partially used for recess (4)
I believe the answer is:
apse
'for recess' is the definition.
(apse is a kind of recess)
'rap session partially' is the wordplay.
'partially' indicates a hidden word.
'APSE' is hidden within 'rap session'.
'used' acts as a link.
(Other definitions for apse that I've seen before include "Projection to the east end of a church" , "Where you could find a magistrate's chair" , "inside church?" , "Offshoot from the choir, nave or aisle in a church" , "Recess at eastern end of a church" .)