The most common and most likely answer to this crossword clue is the 10 letter word ORANG-UTAN
I've seen this crossword clue in Independent
O
R
A
N
G
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U
T
A
N
More clues leading to the result ORANG-UTAN
- Argonaut novel by New Forest resident
- Ape having nougat ran off
- Sounded from belfry? Oscar climbs there with an ape
- Primate looked after corporation, one presided over by head of order
- Ape cut fruit and chewed a nut
- Primate managed to get godhead into published article
- Before a nut develops, lots of fruit, which may hang from trees
- Fruit endlessly given to posh smart brown ape
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 = orang-utan.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 ORANG-UTAN mean?
ORANG-UTAN noun- An arboreal anthropoid ape genus Pongo consisting of two species, Pongo pygmaeus of Borneo and Pongo abelii of Sumatra, having a shaggy reddish-brown coat, long arms, and no tail.