Run up to Casanova? (4)
I believe the answer is:
wolf
'casanova?' is the definition.
(both can mean a man who seduces women)
'run up' is the wordplay.
'run' becomes 'flow' (synonyms).
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'flow' reversed gives 'WOLF'.
'to' is the link.
(Other definitions for wolf that I've seen before include "Dog-like animal - womaniser" , "Carnivorous mammal" , "Beast, member of pack" , "22A [WILD DOG]" , "Predator that hunts in packs" .)