The most common and most likely answer to this crossword clue is the 6 letter word EAGLED
E
A
G
L
E
D
Buddy explains!
The straight part
We know that "Having scored better than most" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having scored better than most = eagled.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 EAGLED mean?
EAGLED verb- To score an eagle.