Solemnly promise (5)
I believe the answer is:
swear
'solemnly promise' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for swear that I've seen before include "Utter obscenities or take an oath" , "Solemnly promise" , "Assert" , "Express annoyance" , "Avow" .)