Cap on British tree production (5)
I believe the answer is:
beret
'cap' is the definition.
(I know that beret is a type of cap)
'on british tree production' is the wordplay.
'on' indicates putting letters inside (as in clothing 'on' a person).
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'production' indicates an anagram.
'tree' is an anagram of 'eret'.
'b' inserted into 'eret' is 'BERET'.
(Other definitions for beret that I've seen before include "item of headwear" , "Soft round cap without a peak" , "Kind of floppy cap with no peak" , "felt on one's head" , "Flat French cap" .)