Promise Oscar a little time with husband (4)
I believe the answer is:
oath
'promise' is the definition.
(I know that oath is a type of promise)
'oscar a little time with husband' is the wordplay.
'oscar' becomes 'O' (phonetic alphabet: alpha, bravo, charlie etc.).
'little time' becomes 't' (abbreviation for time).
'with' means one lot of letters go next to another.
'husband' becomes 'h' (abbreviation).
'o'+'a'+'t'+'h'='OATH'
(Other definitions for oath that I've seen before include "gadzooks!" , "Courtroom promise" , "blasphemy" , "Commitment to tell the truth" , "One sworn" .)