Dark period with good hearts suppressed by idiot (5)
I believe the answer is:
night
'dark period' is the definition.
(period of the day when it's dark)
'good hearts suppressed by idiot' is the wordplay.
'good' becomes 'g' (abbreviation).
'hearts' becomes 'h' (abbreviation used in card games e.g. bridge).
'suppressed by' indicates putting letters inside (I've seen this in other clues).
'idiot' becomes 'nit' (nit can mean a stupid person).
'g'+'h'='gh'
'gh' inserted into 'nit' is 'NIGHT'.
'with' is the link.
(Other definitions for night that I've seen before include "Saturday -- Fever (film)" , "Illumination needed now" , "Thing (anag)" , "For most, the time for sleep" , "late" .)