Admit us running into arena (7)
I believe the answer is:
stadium
'arena' is the definition.
(I know that Stadium is a type of arena)
'admit us running' is the wordplay.
'running' is an anagram indicator.
'admit'+'us'='admitus'
'admitus' with letters rearranged gives 'STADIUM'.
'into' is the link.
(Other definitions for stadium that I've seen before include "Sports arena" , "eg Yankee, Wembley" , "Venue for sporting events, concerts etc" , "Open-air sports venue" , "bowl?" .)