Courting daughter with giant fiddle (6)
I believe the answer is:
'courting' is the definition.
(both mean seeing someone romantically)
'daughter with giant fiddle' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'with' says to put letters next to each other.
'fiddle' indicates anagramming the letters.
'giant' with letters rearranged gives 'ating'.
(Other definitions for dating that I've seen before include "Seeing" , "Taking out" , "Going steady" , "Going out with (a person)" , "Imposing time code or keeping social engagement" .)