Wife greeting claims about being playful (9)
I believe the answer is:
whimsical
'playful' is the definition.
(thesaurus)
'wife greeting claims about' is the wordplay.
'wife' becomes 'w' (abbreviation).
'greeting' becomes 'hi' (hi is a kind of greeting).
'about' indicates anagramming the letters.
'claims' is an anagram of 'msical'.
'w'+'hi'+'msical'='WHIMSICAL'
'being' acts as a link.
(Other definitions for whimsical that I've seen before include "Mischievous" , "Fanciful or playful" , "Playfully fanciful" , "Appealingly fanciful" , "Playfully quaint" .)