The most common and most likely answer to this crossword clue is the 7 letter word HUNTERS
H
U
N
T
E
R
S
More clues leading to the result HUNTERS
Buddy explains!

The straight part
We know that "Watches/people going after game" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case watches/people going after game = hunters.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 HUNTERS mean?
HUNTERS noun- One who hunts game for sport or for food; a huntsman or huntswoman.
- A dog used in hunting.
- A horse used in hunting, especially a thoroughbred, bred and trained for hunting.
- One who hunts or seeks after anything.
- A person who bottles up their aggression and eventually releases it explosively.
- A kind of spider, the huntsman or hunting spider.
- A pocket watch with a spring-hinged circular metal cover that closes over the dial and crystal, protecting them from dust and scratches.