The most common and most likely answer to this crossword clue is the 11 plus 3 letter word NEANDERTHAL MAN
I've seen this crossword clue in The Daily Telegraph
N
E
A
N
D
E
R
T
H
A
L
M
A
N
More clues leading to the result NEANDERTHAL MAN
- Mr Handel, neat in composition, meets an old cave-dweller.
- Primitive criminal alarmed, then arrested by old lady
- Distant cousin cultivating the land near isle
- Surprisingly maternal, Anne Hathaway’s daughter, initially a reactionary person
- Worked meaner land than earlier people
- An alderman then becomes a reactionary person?
- Lost name brought to enthral DNA analysis, old chap!
- An alderman then relocated — lived in Europe long time ago
- Primitive sort near the land by isle
Buddy explains!

The straight part
We know that "Primitive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case primitive = neanderthal man.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.