Competitions set to run with man well organised (11)
I believe the answer is:
tournaments
'competitions' is the definition.
(tournament is a kind of competition)
'set to run with man well organised' is the wordplay.
'with' means one lot of letters go next to another.
'well organised' is an anagram indicator.
'set'+'to'+'run'+'man'='settorunman'
'settorunman' is an anagram of 'TOURNAMENTS'.
(Other definitions for tournaments that I've seen before include "Jousting events" , "competitive events" .)