British burden to provide incentive (5)
I believe the answer is:
bonus
'incentive' is the definition.
(synonyms)
'british burden' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'burden' becomes 'onus' (synonyms).
'b'+'onus'='BONUS'
'to provide' is the link.
(Other definitions for bonus that I've seen before include "Honorarium" , "Extra payment for good work" , "Additional incentive payment" , "- generis means unique" , "Premium" .)