Composer’s frightful glare (5)
I believe the answer is:
elgar
'composer's' is the definition.
(Edward Elgar)
'frightful glare' is the wordplay.
'frightful' indicates an anagram (a frightful spelling).
'glare' with letters rearranged gives 'ELGAR'.
(Other definitions for elgar that I've seen before include "Glare critically at the British composer" , "Score-person" , "man of note" , "Enigma Vars. composer" , "13 composer, 1857-1934" .)