After month, test of municipal official (7)
I believe the answer is:
mayoral
'municipal official' is the definition.
Both the answer and definition are adjectives. Perhaps you can see an association between them that I can't see?
'after month test' is the wordplay.
'after' is a charade indicator (letters next to each other).
'month' becomes 'may' (May is an example).
'test' becomes 'oral' (oral is a type of examination).
'may'+'oral' is 'MAYORAL'.
'of' is the link.
Can you help me to learn more?
(Other definitions for mayoral that I've seen before include "Concerned with official" , "Dignitary's" , "Of a civic dignitary" , "Relating to city leader" , "for local official" .)