Part of a lemon (4 letter answer)
The answer PEEL is seen frequently, appearing about once every 120 puzzles.
Emulate an ecdysiast
Lose a layer
Something to slip on?
Strip bark from
Suffer from sunburn
Do burlesque work
Eponym of London's bobbies
Eponymous British Bobby
"Father of London's bobbies"
Leave rubber, with "out"
Lose one's sunburn
Result of a day at the beach?
Result of a burn
What strippers do
Founder of Britain's Conservative Party
Sir Robert of London's bobbies
PEEL as a noun:
1. (skin, rind, peel) = the tissue forming the hard outer layer (of e.g. a fruit)
2. (Peel, Robert Peel, Sir Robert Peel) = British politician (1788-1850)
3. (peel, skin) = the rind of a fruit or vegetable
PEEL as a verb:
1. (skin, peel, pare) = strip the skin off; "pare apples"
2. (peel off, peel, flake off, flake) = come off in flakes or thin small pieces; "The paint in my house is peeling off"
3. (undress, discase, uncase, unclothe, strip, strip down, disrobe, peel) = get undressed; "please don't undress in front of everybody!"; "She strips in front of strangers every night for a living"