The most common and most likely answer to this crossword clue is the 8 letter word ENCOMION
E
N
C
O
M
I
O
N
Buddy explains!
The straight part
We know that "great praise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case great praise = encomion.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.