After exam, one finally has a ball (6)
I believe the answer is:
testis
'a ball' is the definition.
('testis' can be a synonym of 'ball')
'after exam one finally has' is the wordplay.
'after' is a charade indicator (letters next to each other).
'exam' becomes 'test' ('test' can be a synonym of 'exam').
'one' becomes 'i' (Roman numeral**).
'finally' suggests the final letters.
The final letter of 'has' is 's'.
'test' next to 'i' is 'testi'.
'testi'+'s'='TESTIS'
(Other definitions for testis that I've seen before include "Nut" , "ball" .)