Spice put in after cold rum? Not right (5)
I believe the answer is:
cumin
'spice' is the definition.
(cumin is a spice)
'in after cold rum? not right' is the wordplay.
'after' is a charade indicator (letters next to each other).
'cold' becomes 'c' (eg on taps).
'not' indicates named letters should be taken away.
'right' becomes 'r' (common abbreviation).
'rum' with 'r' removed is 'um'.
'c'+'um'='cum'
'in' put after 'cum' is 'CUMIN'.
'put' is the link.
(Other definitions for cumin that I've seen before include "Spice used in curries" , "seasoning" , "Aromatic (curry) spice" , "relief from wind" , "Aromatic seeds used in cooking" .)