Promise a hot soup (4)
I believe the answer is:
oath
'promise' is the definition.
(I know that Oath is a type of promise)
'a hot soup' is the wordplay.
'soup' indicates an anagram.
'a'+'hot'='ahot'
'ahot' anagrammed gives 'OATH'.
(Other definitions for oath that I've seen before include "Imprecation" , "bad language" , "What frustrated people say" , "swearing" , "Courtroom promise" .)