Entrance with a final bit of cold calling (9)
I believe the answer is:
admission
'entrance' is the definition.
(I know that admission is a type of entrance)
'a final bit of cold calling' is the wordplay.
'final bit of' indicates one should take the final letters.
'calling' becomes 'mission' (I've seen this in other clues).
The final letter of 'cold' is 'd'.
'a'+'d'+'mission'='ADMISSION'
'with' acts as a link.
(Other definitions for admission that I've seen before include "concession" , "A confessing" , "Access" , "yield confession of sin maybe" , "Right to enter" .)