Sponsor sporting venue in the circumstances (10)
I believe the answer is:
background
'the circumstances' is the definition.
'sponsor sporting venue' is the wordplay.
'sponsor' becomes 'back'.
'sporting venue' becomes 'ground' (eg a football ground).
'back'+'ground'='BACKGROUND'
'in' is the link.
(Other definitions for background that I've seen before include "history" , "player's obscure position" , "inconspicuous position" , "Unobtrusive element" , "kind of music" .)