Victor and Oscar get married, having made a solemn promise (5)
I believe the answer is:
vowed
'made a solemn promise' is the definition.
(I've seen this in another clue)
'victor and oscar get married' is the wordplay.
'victor' becomes 'V' (phonetic alphabet: alpha, bravo, charlie etc.).
'and' says to put letters next to each other.
'oscar' becomes 'O' (phonetic alphabet: alpha, bravo, charlie etc.).
'get married' becomes 'wed' (synonyms).
'v'+'o'+'wed'='VOWED'
'having' is the link.
(Other definitions for vowed that I've seen before include "Solemnly promised" , "Made a promise" , "Solemnly pledged" , "took the pledge" .)