Councillor is given a large container for neckwear (6)
I believe the answer is:
cravat
'for neckwear' is the definition.
(cravat is a kind of neckwear)
'councillor is given a large container' is the wordplay.
'councillor' becomes 'cr' (abbreviation).
'is given' is a charade indicator (letters next to each other).
'large container' becomes 'vat' (I've seen this before).
'cr'+'a'+'vat'='CRAVAT'
(Other definitions for cravat that I've seen before include "Fine quality scarf" , "Neckcloth" , "Cloth for the neck" , "item of clothing" , "Strip of fabric worn round the neck" .)