The most common and most likely answer to this crossword clue is the 8 letter word UPSTAGED
I've seen this crossword clue in The Daily Telegraph
U
P
S
T
A
G
E
D
Buddy explains!
The straight part
We know that "Went back to secure an advantage over a fellow player" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case went back to secure an advantage over a fellow player = upstaged.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 UPSTAGED mean?
UPSTAGED verb- To draw attention away from others, especially on-stage.
- To force other actors to face away from the audience by staying upstage.
- To treat snobbishly.
- To restage (cancer) to a higher stage than that found at last assessment (compare downstage).