Praise one's former spouse, maybe a lot (5)
I believe the answer is:
extol
'praise one's' is the definition.
'extol' can be an answer for 'praise' (extolling is a kind of praising). I'm unsure of the 'one's' bit.
'former spouse maybe a lot' is the wordplay.
'former spouse' becomes 'ex' (an ex-spouse).
'maybe' indicates anagramming the letters.
'lot' is an anagram of 'tol'.
'ex'+'tol'='EXTOL'
Can you help me to learn more?
(Other definitions for extol that I've seen before include "Glorify - honour" , "Say great things about" , "Praise enthusiastically" , "Lift up" , "Lavishly praise" .)