The most common and most likely answer to this crossword clue is the 5 letter word EXTOL
I've seen this crossword clue in The Times
E
X
T
O
L
More clues leading to the result EXTOL
- Former partner not entirely mentioned for praise
- Praise levy once cut
- Praise old charge, endlessly
- Praise almost imparted by husband once
- Praise, employing some pretext, oligarch
- Passionately praise old auction item coming up
- Acclaim former tax reduced by one pound
- Speak highly of former tax cut
- . Celebrate former partner’s reversal of fortune
- Praise group coming from Sussex to Leicester
Buddy explains!

The straight part
We know that "praise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case praise = extol.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EXTOL mean?
EXTOL verb- To praise; to make high.