Breaks rest to develop a mode of swimming (12)
I believe the answer is:
breaststroke
'a mode of swimming' is the definition.
'breaks rest to develop' is the wordplay.
'develop' is an anagram indicator.
'breaks'+'rest'+'to'='breaksrestto'
'breaksrestto' anagrammed gives 'BREASTSTROKE'.
(Other definitions for breaststroke that I've seen before include "Natant style" , "What swimmers may do" , "Adam Peaty's swimming style" .)