Promise of a hot soup (4)
I believe the answer is:
oath
'promise' is the definition.
(I've seen this before)
'a hot soup' is the wordplay.
'soup' indicates anagramming the letters.
'a'+'hot'='ahot'
'ahot' anagrammed gives 'OATH'.
'of' is the link.
(Other definitions for oath that I've seen before include "Sworn declaration" , "word intended?" , "What frustrated people say" , "in court, we take it" , "Curse - sworn statement" .)