Extra responsibility follows job's termination (5)
I believe the answer is:
bonus
'extra' is the definition.
(bonus can mean extra or additional)
'responsibility follows job's termination' is the wordplay.
'responsibility' becomes 'onus' (onus is a duty or responsibility).
'follows' means one lot of letters go next to another.
'termination' indicates one should take the final letters.
The final letter of 'job' is 'b'.
'onus' after 'b' is 'BONUS'.
(Other definitions for bonus that I've seen before include "Honorarium" , "Extra payment for good results" , "Good-performance payment" , "Extra money paid for good performance" , "Additional payment or benefit above the norm" .)