Tree’s end of life? Axe (4)
I believe the answer is:
fire
'axe' is the definition.
(both can mean to dismiss or sack)
'tree's end of life?' is the wordplay.
'tree' becomes 'fir' (fir is a kind of tree).
'end of' says to take the final letters.
The last letter of 'life' is 'e'.
'fir'+'e'='FIRE'
(Other definitions for fire that I've seen before include "Sack; conflagration" , "... or combustion" , "Set light to; shoot" , "Shoot; sack" , "Inspire" .)