The most common and most likely answer to this crossword clue is the 7 letter word BABOONS
I've seen this crossword clue in The Guardian
B
A
B
O
O
N
S
More clues leading to the result BABOONS
Buddy explains!

The straight part
We know that "Primates" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case primates = baboons.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 BABOONS mean?
BABOONS noun- An Old World monkey of the genus Papio, having dog-like muzzles and large canine teeth, cheek pouches, a short tail, and naked callosities on the buttocks.
- A foolish or boorish person.