Remnant of fire at end of three months (5)
I believe the answer is:
ember
This clue could be a double definition.
'remnant of fire' is the first definition.
'ember' can be an answer for 'remnant' (I have seen 'Remnant of bonfire' mean 'ember' so perhaps 'remnant' could also mean 'ember'). I am unsure of the 'of fire' bit.
'end of three months' is the second definition.
(September, November and December)
'at' is the link.
Can you help me to learn more?
(Other definitions for ember that I've seen before include "Fire remnant" , "Wood still burning" , "showing residual fire" , "Remnant of bonfire" , "Glowing cinder" .)