Councillor stupidly alarmed? Not at first (8)
I believe the answer is:
alderman
'councillor' is the definition.
(alderman is a kind of councillor)
'stupidly alarmed? not at first' is the wordplay.
'stupidly' indicates anagramming the letters (a stupid ordering of the letters).
'at first' says to take the initial letters.
The initial letter of 'not' is 'n'.
'alarmed' with letters rearranged gives 'alderma'.
'alderma'+'n'='ALDERMAN'
(Other definitions for alderman that I've seen before include "Local politician" , "Old municipal official" , "Former civic dignitary" , "Member of an English city council" , "In England and Wales, a former senior local councillor" .)