The most common and most likely answer to this crossword clue is the 8 letter word BUSHBABY
I've seen this crossword clue in Financial Times
B
U
S
H
B
A
B
Y
More clues leading to the result BUSHBABY
- Husband in public transport area welcoming black primate
- Child born to Dubya, cute little creature
- Young Kate a cute creature
- Primate hard at work catching hard black sailor
- Primate — shaggy hair own creation?
- Bug-eyed creature, a crawler as Dubya once was?
- Henry Bishop, seaman apprehended by meddling primate
- Quiet British sailor in exchange involving money and African islander
- Perhaps, what Dubya once was... a primate!
Buddy explains!

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 BUSHBABY mean?
BUSHBABY noun- An small, nocturnal, African primate, similar to a lemur.