Cooler beat for ardent ardmirers (3,4)
I believe the answer is:
fan club
'ardent ardmirers' is the definition.
I can't tell whether this definition defines the answer.
'cooler beat' is the wordplay.
'cooler' becomes 'fan' (something which cools).
'beat' becomes 'club' (to hit with a club).
'fan'+'club'='FAN CLUB'
'for' is the link.
Can you help me to learn more?
(Other definitions for fan club that I've seen before include "Organised supporters' group" , "Association of devotees" , "Band of followers" , "Admiration society" , "Group of admirers as for pop star" .)