Remove old unsafe sick tree tops (4)
I believe the answer is:
oust
'remove' is the definition.
(I know that oust is a more specific form of the action remove)
'old unsafe sick tree tops' is the wordplay.
'tops' suggests taking the first letters.
The initial letters of 'old unsafe sick tree' is 'OUST'.
(Other definitions for oust that I've seen before include "Overthrow" , "Drive out, eject from office" , "Unseat" , "Show the door to" , "Turf out" .)