The most common and most likely answer to this crossword clue is the 6 letter word RHESUS
I've seen this crossword clue in Financial Times
R
H
E
S
U
S
More clues leading to the result RHESUS
- Monkey rushes out
- Man is breaking most of biscuit for primate
- Monkey King, in Greek mythology
- Primate replaced ushers
- Primate’s right-hand manshunning judge
- Monkey rushes out of its tree?
- He’s trapped in crush lacking protection for primate
- Blood factor needed in unit reviving patients around hospital
- Take man to discover monkey
- Primate‘s right hand suppressing potential uses
Buddy explains!
The straight part
We know that "primate" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case primate = rhesus.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.