Coal remaining at the end of three months (5)
I believe the answer is:
ember
I believe this clue is a double definition.
'coal remaining' is the first definition.
'the end of three months' is the second definition.
(September, November and December)
'at' is the link.
(Other definitions for ember that I've seen before include "Glowing, smouldering piece of coal or wood" , "Material in dying fire" , "Remnant of bonfire" , "Small piece of glowing coal in a dying fire" , "Just a glimmer" .)