Right to run around middle distance (5)
I believe the answer is:
girth
'middle distance' is the definition.
(measurement around something's middle)
'right to run' is the wordplay.
'to run' is an anagram indicator.
'right' is an anagram of 'GIRTH'.
'around' acts as a link.
(Other definitions for girth that I've seen before include "Distance round a body" , "Perimeter" , "Band around a horse's belly" , "The distance around a thing or tummy" , "Distance round the middle" .)