Admit a pledge (4)
I believe the answer is:
avow
'admit' is the definition.
(avowing is a kind of admiting)
'a pledge' is the wordplay.
'pledge' becomes 'vow' (vowing is a kind of pledging).
'a'+'vow'='AVOW'
(Other definitions for avow that I've seen before include "Declare a promise of fidelity at the altar" , "Assert - admit" , "Strongly maintain" , "Asseverate" , "Solemnly promise" .)