The most common and most likely answer to this crossword clue is the 3 letter word NIT
I've seen this crossword clue in The Daily Telegraph
N
I
T
More clues leading to the result NIT
Buddy explains!

The straight part
We know that "split hairs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case split hairs = nit.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 NIT mean?
NIT noun- The egg of a louse.
- A young louse.
- A head louse regardless of its age.
- A fool, a nitwit.
- A nitpicker.
- A minor shortcoming.
- A candela per square meter.
- A spirit in Burmese mythology, whose cult is followed alongside Buddhism.
- A logarithmic unit of information or entropy, based on natural logarithms.