The odd beauty from club (3)
I believe the answer is:
bat
'club' is the definition.
(as in sporting equipment)
'the odd beauty' is the wordplay.
'the odd' indicates alternate letters.
The alternate letters of 'beauty' are 'BAT'.
'from' is the link.
(Other definitions for bat that I've seen before include "Flutter (eyelids)" , "Club used in cricket" , "Wooden implement for cricket" , "Small flying mammal, may be vampire" , "Night-flyer" .)