The most common and most likely answer to this crossword clue is the 4 letter word FOIL
I've seen this crossword clue in The Daily Telegraph
F
O
I
L
Buddy explains!
The straight part
We know that "Wrap/hamper" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case wrap/hamper = foil.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 FOIL mean?
FOIL noun- A very thin sheet of metal.
- Thin aluminium/aluminum (or, formerly, tin) used for wrapping food.
- A thin layer of metal put between a jewel and its setting to make it seem more brilliant.
- (authorship) In literature, theatre/theater, etc., a character who helps emphasize the traits of the main character and who usually acts as an opponent or antagonist.
- Anything that acts by contrast to emphasise the characteristics of something.
- A very thin sword with a blunted (or foiled) tip
- A thin, transparent plastic material on which marks are made and projected for the purposes of presentation. See transparency.
- A stylized flower or leaf.
- A hydrofoil.
- An aerofoil/airfoil.
- To cover or wrap with foil.
- Failure when on the point of attainment; defeat; frustration; miscarriage.
- One of the incorrect answers presented in a multiple-choice test.
- To prevent (something) from being accomplished.
- To prevent (someone) from accomplishing something.
- To blunt; to dull; to spoil.
- To tread underfoot; to trample.
- The track of an animal.
- To expand a product of two or more algebraic expressions, typically binomials.
- To defile; to soil.