Admit, own up (7)
I believe the answer is:
confess
This clue is a double definition.
'admit' is the first definition.
(I know that confess is a more specific form of the action admit)
'own up' is the second definition.
(I've seen this in another clue)
(Other definitions for confess that I've seen before include "Admit (to wrongdoing)" , "Plead guilty (in order to receive absolution?)" , "Tell a priest one's sins" , "Admit (to crime)" , "Concede" .)