Conservative tier boast (4)
I believe the answer is:
crow
'boast' is the definition.
(crowing is a kind of boasting)
'conservative tier' is the wordplay.
'conservative' becomes 'c' (abbreviation commonly used in UK politics).
'tier' becomes 'row' (eg a row of seats at a theatre).
'c'+'row'='CROW'
(Other definitions for crow that I've seen before include "Native American -- bird" , "Black bird; boast" , "Brag; carrion bird" , "Make sound of cock - bird" , "Express gleeful triumph" .)