Branch is 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'
'is' acts as a link.
(Other definitions for offshoot that I've seen before include "Branch attached to the main stem" , "Development" , "sequel?" , "Small branch growing from the main stem" , "Branch, derivative" .)