A tune playing about king's personality (6)
I believe the answer is:
nature
'personality' is the definition.
(thesaurus)
'a tune playing about king's' is the wordplay.
'playing' is an anagram indicator.
'about' means one lot of letters goes inside another.
'king' becomes 'R' (abbreviation for rex, king in Latin).
'a'+'tune'='atune'
'atune' anagrammed gives 'natue'.
'natue' going around 'r' is 'NATURE'.
(Other definitions for nature that I've seen before include "Essential qualities or characteristics" , "sort of reserve" , "- Study; - reserve" , "Character (of a person or thing)" , "mother, so-called" .)