Finally, did you accept any responsibility? (4)
I believe the answer is:
duty
'responsibility?' is the definition.
('duty' can be a synonym of 'responsibility')
'finally did you accept any' is the wordplay.
'finally' says to take the final letters.
The last letters of 'did you accept any' are 'DUTY'.
(Other definitions for duty that I've seen before include "form of tax" , "Tariff" , "Obligatory task(s) - tax" , "'Obligation, responsibility (4)'" , "Service - tax - obligation" .)