The most common and most likely answer to this crossword clue is the 7 letter word CUTICLE
I've seen this crossword clue in Financial Times
C
U
T
I
C
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E
More clues leading to the result CUTICLE
- Be effective after all, maybe, protecting large layer of skin
- Bit of skin trimmed and left in freezer
- Mentioned child’s dainty little bit of toe?
- Dead skin around base of nail attractive girl describes
- Audible reminder to stimulate skin
- Attractive person grasps oddly cold skin
- Sliced dessert, filled with milky centre, forms thin skin
- Seen at the base of nail — lice cut into bits
- Reportedly assist with an act to stimulate the skin around a nail
Buddy explains!

The straight part
We know that "Dead skin" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dead skin = cuticle.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 CUTICLE mean?
CUTICLE noun- The outermost layer of the skin of vertebrates; the epidermis.
- The strip of hardened skin at the base and sides of a fingernail or toenail.
- Dead or cornified epidermis.
- A noncellular protective covering outside the epidermis of many invertebrates and plants.
- A thin skin formed on the surface of a liquid.