Like a type of music exam taken after church (6)
I believe the answer is:
choral
'like a type of music' is the definition.
'taken after church' is the wordplay.
'taken' becomes 'oral' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'after' means one lot of letters go next to another.
'church' becomes 'ch' (common abbreviation).
'oral' after 'ch' is 'CHORAL'.
'exam' is the link.
This may not be right. It may belong to another bit of the clue.
(Other definitions for choral that I've seen before include "Involving many singers" , "Sung by a band of singers" , "Sung psalm" , "... his ninth ..." , "Pertaining to a group of singers" .)