The most common and most likely answer to this crossword clue is the 5 letter word CHIMP
C
H
I
M
P
More clues leading to the result CHIMP
- Primate's mischievous child overwhelmed by church
- X marks place at the start for primate
- Mischief-maker chasing child’s a little monkey
- Deep-fried potato containing head of minute animal
- Devil stalking chief primate
- You may see me involved in much impishness
- Primate briefly places church above devil
- Ape Greek character, Member of Parliament
- Fellow sees I am standing for a close relative of ours
- Ch-cheeky monkey?
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 = chimp.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 CHIMP mean?
CHIMP verb- To review each image on a digital camera after it is taken.
- To get very excited when showing images on a digital camera.
- A species of great ape in the genus Pan, native to Africa, and believed by biologists to be the closest extant relative to humans.