Promised solemnly (5)
I believe the answer is:
swore
'promised solemnly' is the definition.
('swear' can be a synonym of 'promise solemnly')
This is the entire clue.
(Other definitions for swore that I've seen before include "Blasphemed" , "Took oath or cursed" , "used bad language" , "Uttered profanities or avowed" .)