Host’s crazy banning British (4)
I believe the answer is:
army
'host's' is the definition.
(I've seen this before)
'crazy banning british' is the wordplay.
'crazy' becomes 'barmy' (I've seen this before).
'banning' suggests deleting specific letters.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'barmy' with 'b' taken out is 'ARMY'.
(Other definitions for army that I've seen before include "Large military body" , "See 17" , "Body of people organised for war" , "Collective term for caterpillars" , "See 21" .)