Interested to rewrite rigid tune (9)
I believe the answer is:
intrigued
'interested' is the definition.
(intriguing is a kind of interesting)
'rewrite rigid tune' is the wordplay.
'rewrite' indicates an anagram.
'rigid'+'tune'='rigidtune'
'rigidtune' with letters rearranged gives 'INTRIGUED'.
'to' acts as a link.
(Other definitions for intrigued that I've seen before include "Becoming interested" , "Having curiosity aroused" , "Keenly interested" .)