Follow with hearts in suit (5)
I believe the answer is:
chase
'follow' is the definition.
(I know that chase is a kind of follow)
'hearts in suit' is the wordplay.
'hearts' becomes 'h' (abbreviation used in card games e.g. bridge).
'in' indicates putting letters inside.
'suit' becomes 'case' (synonyms).
'h' put within 'case' is 'CHASE'.
'with' acts as a link.
(Other definitions for chase that I've seen before include "Pursue, run after" , "Follow" , "Hurry" , "grave, as before?" , "Engrave - hunt - pursue" .)