One with cold admitted to AE (3)
I believe the answer is:
ace
'one' is the definition.
(ace has a value of one in some card games)
'cold admitted to ae' is the wordplay.
'cold' becomes 'C' (eg on taps).
'admitted to' indicates putting letters inside.
'c' put within 'ae' is 'ACE'.
'with' acts as a link.
(Other definitions for ace that I've seen before include "Excellent" , "Top card or winning tennis serve" , "Great" , "Expert; one" , "single > club > champion" .)