The most common and most likely answer to this crossword clue is the 4 letter word HAIR
H
A
I
R
More clues leading to the result HAIR
- Likely to go off with the least amount of a shock?
- Hot wind causes shock
- Waking after locks triggering alarm
- Musical atmosphere met by Handel at first
- Musical — crowning glory perhaps?
- Musical chairs, first and last to go
- A very short distance from Bath has rider struggling
- Initially hostile atmosphere that grows on one
- Hitchcock's first appearance at what's announced as cutting-edge horror film?
- 13 creating frisson of fear just before 2
Buddy explains!

The straight part
We know that "grows on one" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case grows on one = hair.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 HAIR mean?
HAIR noun- A pigmented filament of keratin which grows from a follicle on the skin of humans and other mammals.
- The collection or mass of such growths growing from the skin of humans and animals, and forming a covering for a part of the head or for any part or the whole body.
- A slender outgrowth from the chitinous cuticle of insects, spiders, crustaceans, and other invertebrates. Such hairs are totally unlike those of vertebrates in structure, composition, and mode of growth.
- A cellular outgrowth of the epidermis, consisting of one or of several cells, whether pointed, hooked, knobbed, or stellated.
- A locking spring or other safety device in the lock of a rifle, etc., capable of being released by a slight pressure on a hair-trigger.
- Haircloth; a hair shirt.
- Any very small distance, or degree; a hairbreadth.
- Complexity; difficulty; quality of being hairy
- To remove the hair from.
- To grow hair (where there was a bald spot).
- To cause to have hair; to provide with hair
- To string the bow for a violin.