Extra cash, not British, becomes burden (4)
I believe the answer is:
onus
'burden' is the definition.
(synonyms)
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for onus that I've seen before include "'Burden, of proof (4)'" , "Responsibilty" , "'Burden, load (4)'" , "Obligation - charge" , "'Responsibility, task or burden (4)'" .)