Praise one’s former partner up 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 am not sure about the 'one's' bit.
'former partner up a lot' is the wordplay.
'former partner' becomes 'ex'.
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'lot' reversed gives 'tol'.
'ex'+'tol'='EXTOL'
Can you help me to learn more?
(Other definitions for extol that I've seen before include "Say great things about" , "Sing the praises of" , "Pay tribute to" , "Lavishly praise" , "Warmly approve of" .)