Puzzling any old guy or girl (5,4)
I believe the answer is:
young lady
'girl' is the definition.
(I know that girl can be written as young lady)
'puzzling any old guy' is the wordplay.
'puzzling' is an anagram indicator.
'any'+'old'+'guy'='anyoldguy'
'anyoldguy' anagrammed gives 'YOUNG LADY'.
'or' is the link.
(Other definitions for young lady that I've seen before include "Sweetheart" , "Maiden" .)