Shunning red, Chelsea ran around their rivals (7)
I believe the answer is:
arsenal
'their rivals' is the definition.
I can't tell whether this definition defines the answer.
'shunning red chelsea ran around' is the wordplay.
'shunning' is a deletion indicator.
'red' becomes 'che' (Che Guevara the Marxist revolutionary).
'around' indicates an anagram.
'chelsea'+'ran'='chelsearan'
'chelsearan' with 'che' removed is 'lsearan'.
'lsearan' anagrammed gives 'ARSENAL'.
(Other definitions for arsenal that I've seen before include "Gunners of North London" , "munitions factory" , "Store of guns and ammunition" , "English football club and military depot" , "Military store for arms, ammunition etc" .)