Composer taking brief holidays by the end of August (5)
I believe the answer is:
holst
'composer' is the definition.
(Gustav Holst)
'brief holidays by the end of august' is the wordplay.
'brief holidays' becomes 'hols' (informal abbreviation; 'brief' indicates an abbreviation).
'by' says to put letters next to each other.
'the end of' suggests the final letters.
The last letter of 'august' is 't'.
'hols'+'t'='HOLST'
'taking' acts as a link.
(Other definitions for holst that I've seen before include "Scorer" , "Gustav --, English composer" , "Composer of The Planets, d. 1934" , "He scored" , "Planets Suite composer" .)