Lyric is rewritten by him (5)
I believe the answer is:
cyril
'him' is the definition.
'lyric is rewritten' is the wordplay.
'is rewritten' indicates an anagram (I've seen 'being rewritten' mean this).
'lyric' anagrammed gives 'CYRIL'.
'by' acts as a link.
(Other definitions for cyril that I've seen before include "Reputed saintly inventor of the Russian alphabet" , "Saint said to have created the Russian alphabet" .)