The most common and most likely answer to this crossword clue is the 3 plus 4 letter word FAT CAMP
I've seen this crossword clue in The Times
F
A
T
C
A
M
P
More clues leading to the result FAT CAMP
Buddy explains!
The straight part
We know that "it seeks reduction in visitors" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case it seeks reduction in visitors = fat camp.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.