Bank ignoring prohibition to irritate church (4)
I believe the answer is:
kirk
'church' is the definition.
(kirk is a kind of church)
'bank ignoring prohibition to irritate' is the wordplay.
'ignoring' indicates named letters should be taken away.
'prohibition' becomes 'ban' (ban is a kind of prohibition).
'to irritate' becomes 'irk' (I've seen this before).
'bank' with 'ban' taken out is 'k'.
'k'+'irk'='KIRK'
(Other definitions for kirk that I've seen before include "Church of Scotland" , "Star Trek captain - Scottish church" , "Scots church" , "Presbyterian building?" .)