The most common and most likely answer to this crossword clue is the 8 letter word RACEGOER
I've seen this crossword clue in The Guardian
R
A
C
E
G
O
E
R
More clues leading to the result RACEGOER
Buddy explains!

The straight part
We know that "visitor to Newmarket?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case visitor to newmarket? = racegoer.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 RACEGOER mean?
RACEGOER noun- One who attends horse races or dog races.