Just the character to go hungry about a quarter of an hour (5)
I believe the answer is:
faust
'just the character' is the definition.
I can't tell whether this definition defines the answer.
'go hungry about a quarter of an hour' is the wordplay.
'go hungry' becomes 'fast' (I've seen this before).
'about' indicates putting letters inside.
'a quarter of an hour' becomes 'u' (I can't explain this - if you can you should give a lot more credence to this answer).
'fast' enclosing 'u' is 'FAUST'.
'to' is the link.
Can you help me to learn more?
(Other definitions for faust that I've seen before include "Tragic figure" , "Goethe play" , "Alchemist" , "Opera" , "He sold his soul to the Devil in exchange for knowledge" .)