Tree, say, hugged by British eccentric (9)
I believe the answer is:
butternut
'tree' is the definition.
(butternut is a kind of tree)
'say hugged by british eccentric' is the wordplay.
'say' becomes 'utter' (I've seen this before).
'hugged by' is an insertion indicator (I've seen this in other clues).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'eccentric' becomes 'nut' (nut is a kind of eccentric**).
'b'+'nut'='bnut'
'utter' put into 'bnut' is 'BUTTERNUT'.
(Other definitions for butternut that I've seen before include "sort of a squash" , "species of tree" , "Variety of pumpkin" , "Wood" .)