The most common and most likely answer to this crossword clue is the 4 letter word TOPI
T
O
P
I
More clues leading to the result TOPI
- Protective headgear — one with peak in front
- Pith helmet — most superior one
- Lightweight hat — best on island
- Pith helmet, best one
- Head may have one
- Sunscreen and singlet I put on
- Sun-helmet - most superior one
- Head covering subject, having left college
- Superior individual takes cover in the heat
- Hat that’s best on international
Buddy explains!

The straight part
We know that "Head may have one" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case head may have one = topi.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 TOPI mean?
TOPI noun- An antelope of the species Damaliscus korrigum.
- A taqiyah (skullcap worn by Muslims etc.)