Constant frost beginning to abate in peninsula (6)
I believe the answer is:
crimea
'peninsula' is the definition.
(Crimea is an example)
'constant frost beginning to abate' is the wordplay.
'constant' becomes 'c' (mathematical abbreviation).
'frost' becomes 'rime' (synonyms).
'beginning to' indicates taking the first letters.
The initial letter of 'abate' is 'a'.
'c'+'rime'+'a'='CRIMEA'
'in' is the link.
(Other definitions for crimea that I've seen before include "Peninsula in today's Ukraine, site of an 1853-6 war" , "European peninsula" , "'Ukrainian peninsula, site of a 19th-century war (6)'" , "Scene of the charge of the Light Brigade" , "old war zone" .)