Triumph over former partner in the last month (5)
I believe the answer is:
exult
'triumph' is the definition.
(synonyms)
'over former partner in the last month' is the wordplay.
'over former partner in' becomes 'ex' (I can't justify this - if you can you should give a lot more credence to this answer).
'the last month' becomes 'ult' (short for 'last month' in correspondence).
'ex'+'ult'='EXULT'
Can you help me to learn more?
(Other definitions for exult that I've seen before include "Be intensely joyful" , "Rejoice intensely" , "Crow in triumph" , "Feel or express triumph" , "Rejoice exceedingly, glory in (5)" .)