The most common and most likely answer to this crossword clue is the 9 letter word EPIDERMIS
I've seen this crossword clue in The Times
E
P
I
D
E
R
M
I
S
More clues leading to the result EPIDERMIS
- I simpered awkwardly, showing skin
- In mire, spied damaged layer of skin
- Outermost layer is primed to disintegrate after input of energy
- Skin layer from duck, breached by pressure spray briefly
- English hairstyle I'd adopted is what protects us?
- Side with marks, ripe bananas showing surface
- This, wasting time, spider mite frantically chewed?
- Hide when per diem is lost
- Layer of skin from duck, punctured by power spray briefly
- Fancy rim is deep, which is not skin-deep
Buddy explains!

The straight part
We know that "surface" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case surface = epidermis.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 EPIDERMIS mean?
EPIDERMIS noun- The outer, protective layer of the skin of vertebrates, covering the dermis
- The similar outer layer of cells in invertebrates and plants