Clue: ''Women possibly given a frosty reception' (9)
I believe the answer is:
unwelcome
'given a frosty reception' is the definition.
'clue 'women possibly' is the wordplay.
'possibly' indicates anagramming the letters.
'clue'+'women'='cluewomen'
'cluewomen' is an anagram of 'UNWELCOME'.
(Other definitions for unwelcome that I've seen before include "No received with pleasure - by host?" , "Not gladly received" , "Not wanted" , "Not greeted or received with pleasure, quite the opposite" , "Causing displeasure" .)