Onset of extra time keeps football team going (4)
I believe the answer is:
exit
'going' is the definition.
(exit is a kind of going)
'onset of extra time keeps football team' is the wordplay.
'onset of' says to take the initial letters.
'keeps' indicates putting letters inside.
'football team' becomes 'xi' (I've seen this in other clues).
The initial letters of 'extra time' is 'et'.
'et' going around 'xi' is 'EXIT'.
(Other definitions for exit that I've seen before include "Player's departure" , "Move out" , "Withdrawal" , "Departure of actor" , "Leave the stage" .)