British shirking extra responsibility (4)
I believe the answer is:
onus
'responsibility' is the definition.
(onus is a duty or responsibility)
'british shirking extra' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'shirking' suggests deleting specific letters ('shirk' can mean 'ignore' or 'dodge').
'extra' becomes 'bonus' (I've seen this before).
'bonus' with 'b' taken away is 'ONUS'.
(Other definitions for onus that I've seen before include "Weight of responsibility" , "Obligation - charge" , "Liability" , "Encumbrance" , "'Burden, of proof (4)'" .)