The most common and most likely answer to this crossword clue is the 5 plus 3 letter word SMASH HIT
I've seen this crossword clue in The Guardian
S
M
A
S
H
H
I
T
More clues leading to the result SMASH HIT
- Ways to knock out another successful play?
- Potato dish consumed in quiet: it’s a great success!
- Successful record beaten after defeat
- Great success of mum’s two husbands described by brood
- This ham’s performing blockbuster
- Two instructions to be violent to achieve great success
- Great success — army programme stops this getting out of hand
- Quiet sex appeal gets hospital series to become a great success
- This strangely gripping old TV series seen as a big success
- This ham’s potentially a huge success
Buddy explains!

The straight part
We know that "great success" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case great success = smash hit.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.