Extra money's not Britain's responsibility (4)
I believe the answer is:
onus
'responsibility' is the definition.
(thesaurus)
'extra money's not britain's' is the wordplay.
'extra money's' becomes 'bonuss'.
'not' indicates named letters should be taken away.
'britain's' becomes 'bs' (common abbreviation as in GB).
'bonuss' with 'bs' removed is 'ONUS'.
(Other definitions for onus that I've seen before include "Capulet opponent (R&J)" , "albatross?" , "Liability" , "'Burden, load (4)'" , "Obligation - charge" .)