Competition in sport, with running around (4)
I believe the answer is:
open
'competition' is the definition.
(open is a kind of competition)
'sport with running around' is the wordplay.
'sport with' becomes 'pe' (physical education. I am not sure about the 'with' bit.**).
'running' becomes 'on' (I've seen this in other clues).
'around' means one lot of letters goes inside another.
'pe' inserted inside 'on' is 'OPEN'.
'in' is the link.
(Other definitions for open that I've seen before include "Widely known" , "Candid or unlocked" , "hardly high-security" , "Unfasten" , "golf contest" .)