Capricious wife greeting Hamilton, say, out of uniform (9)
I believe the answer is:
whimsical
'capricious' is the definition.
(synonyms)
'wife greeting hamilton say out of uniform' is the wordplay.
'wife' becomes 'w'.
'greeting' becomes 'hi' (hi is a kind of greeting).
'hamilton say' becomes 'musical' (Hamilton is an example).
'out of' suggests deleting specific letters.
'uniform' becomes 'u' (phonetic alphabet: alpha, bravo, charlie etc.).
'musical' with 'u' taken out is 'msical'.
'w'+'hi'+'msical'='WHIMSICAL'
(Other definitions for whimsical that I've seen before include "Fanciful, fantastical" , "Playfully quaint" , "Playfully fanciful" , "Capricious" , "Quirky" .)