Club's mile champion (4)
I believe the answer is:
mace
'club's' is the definition.
(thesaurus)
'mile champion' is the wordplay.
'mile' becomes 'm' (common abbreviation).
'champion' becomes 'ace' (I've seen this before**).
'm'+'ace'='MACE'
(Other definitions for mace that I've seen before include "Came to get ancient weapon" , "put on the rack?" , "Medieval weapon or kind of spice" , "One of 9 [CLUBS]" , "Spice; heavy club" .)