Nigel excited by new reading material heading off for a seat by the fire (9)
I believe the answer is:
inglenook
'a seat by the fire' is the definition.
(an inglenook is a space by a fireplace)
'nigel excited by new reading material heading off' is the wordplay.
'excited' indicates anagramming the letters.
'by' is a charade indicator (letters next to each other).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'reading material' becomes 'book'.
'heading off' means to remove the first letter.
'book' with its first letter taken off is 'ook'.
'nigel' is an anagram of 'ingle'.
'ingle'+'n'+'ook'='INGLENOOK'
'for' acts as a link.
(Other definitions for inglenook that I've seen before include "warm corner" , "place by fire" , "Medieval fireplace feature" , "Alcove by a large open fire" , "Chimney corner" .)