Swear shelf is under pressure (6)
I believe the answer is:
pledge
'swear' is the definition.
(I know that swear is a more specific form of the action the vow)
'shelf is under pressure' is the wordplay.
'shelf' becomes 'ledge' (synonyms).
'is under' says to put letters next to each other (below, in a down clue).
'pressure' becomes 'p' (abbreviation).
'ledge' put after 'p' is 'PLEDGE'.
(Other definitions for pledge that I've seen before include "Promise or pawn" , "make toast" , "Promise, word of honour" , "Firm commitment" , "Give one's word" .)