Praise former partner for leaving at first (5)
I believe the answer is:
extol
'praise' is the definition.
(extolling is a kind of praising)
'former partner for leaving at first' is the wordplay.
'former partner' becomes 'ex'.
'for' becomes 'to' (I can't explain this - if you can you should believe this answer much more).
'at first' says to take the initial letters.
The first letter of 'leaving' is 'l'.
'ex'+'to'+'l'='EXTOL'
(Other definitions for extol that I've seen before include "be lavish with praise" , "Cry up" , "Warmly approve of" , "Lift up" , "Highly rate" .)