Character is gem but no saint (4)
I believe the answer is:
tone
'character' is the definition.
(tone can mean a character or mood)
'gem but no saint' is the wordplay.
'gem' becomes 'stone' (I've seen this before).
'but no' indicates named letters should be taken away.
'saint' becomes 's'.
'stone' with 's' removed is 'TONE'.
'is' is the link.
(Other definitions for tone that I've seen before include "Quality or character of voice" , "Quality of a musical or vocal sound" , "accent" , "Mood" , "Theobald Wolf . . . ." .)