Kindly reject bitterly cold Frenchman (4)
I believe the answer is:
warm
'kindly' is the definition.
(similar in meaning)
'reject bitterly cold frenchman' is the wordplay.
'reject' says the letters should be written backwards.
'bitterly cold' becomes 'raw' (raw can mean cold or bleak).
'frenchman' becomes 'm' (abbreviation for Monsieur - like 'Mr').
'raw' backwards is 'war'.
'war'+'m'='WARM'
(Other definitions for warm that I've seen before include "On the brink of making discovery" , "Slightly hot" , "Friendly" , "Cordial" , "showing enthusiasm" .)