Former head of agency's upset getting sack (3)
I believe the answer is:
axe
'sack' is the definition.
(both can mean to dismiss or cancel employment)
'former head of agency's upset' is the wordplay.
'former' becomes 'ex' (prefix meaning former or onetime).
'head of' says to take the initial letters.
'upset' says the letters should be written backwards.
The first letter of 'agencys' is 'a'.
'ex'+'a'='exa'
'exa' backwards is 'AXE'.
'getting' is the link.
(Other definitions for axe that I've seen before include "saw alternative?" , "can bring down plane" , "Tool for chopping wood" , "Make redundant" , "Cut costs or staff drastically" .)