Accepting job in government's first, relinquish second (6)
I believe the answer is:
taking
'accepting' is the definition.
(taking is a kind of accepting)
'job in government's first relinquish second' is the wordplay.
'job' becomes 'task' (synonyms).
'government's first' becomes 'g' (1st letter of 'government').
'relinquish' indicates named letters should be taken away.
'second' becomes 's' (common abbreviation).
'task'+'in'+'g'='tasking'
'tasking' with 's' taken away is 'TAKING'.
(Other definitions for taking that I've seen before include "Removing; stealing" , "Extra item added to book" , "acceptance" , "Stealing; charming" , "infectious" .)