Character set out to be most good-hearted (7)
I believe the answer is:
kindest
'most good-hearted' is the definition.
('kind' can be a synonym of 'good-hearted')
'character set out' is the wordplay.
'character' becomes 'kind' (I've seen this before).
'out' indicates anagramming the letters (out can mean wrong or inaccurate).
'set' anagrammed gives 'est'.
'kind'+'est'='KINDEST'
'to be' is the link.
(Other definitions for kindest that I've seen before include "Most agreeable" , "Most benevolent" , "Most compassionate" , "Most considerate" .)