Character up tree that sways (6)
I believe the answer is:
repute
'character' is the definition.
(thesaurus)
'up tree that sways' is the wordplay.
'that sways' indicates an anagram (I've seen 'swaying' mean this (letters swaying or moving around)).
'up'+'tree'='uptree'
'uptree' anagrammed gives 'REPUTE'.
(Other definitions for repute that I've seen before include "State of high regard" , "Character, esteem" , "State of high esteem" , "Up tree (anag)" , "Public standing" .)