Branch not on fire (8)
I believe the answer is:
offshoot
'branch' is the definition.
(I know that branch can be written as offshoot)
'not on fire' is the wordplay.
'not on' becomes 'off' ('off' is the opposite to 'on').
'fire' becomes 'shoot' (shooting is a kind of firing).
'off'+'shoot'='OFFSHOOT'
(Other definitions for offshoot that I've seen before include "Development" , "Side growth" , "Branch; spin-off" , "Branch, derivative" , "Something developing from another" .)