Composer’s vacation close to forest (5)
I believe the answer is:
holst
'composer's' is the definition.
(Gustav Holst)
'vacation close to forest' is the wordplay.
'vacation' becomes 'hols' (I've seen this before).
'close to' suggests the final letters (the close/ending of).
The final letter of 'forest' is 't'.
'hols'+'t'='HOLST'
(Other definitions for holst that I've seen before include "Gustav - (The Planets)" , "Gustav --, English composer" , "Composer of The Planets, d. 1934" , "British composer, 1874-1934" , "Planets Suite composer" .)