The most common and most likely answer to this crossword clue is the 4 letter word DOME
I've seen this crossword clue in The Guardian
D
O
M
E
More clues leading to the result DOME
- 1950s youth going over English millennium building
- Feature of Church maybe — new beginning for Italian capital
- Head seen in random encounter
- Male takes female round London landmark
- Work with engineer in cupola
- Roof party I object to
- Stately edifice rising third
- Roof party — I object below
- Ray’s nearest neighbours in the building
- Make me a structure with a curved roof
Buddy explains!

The straight part
We know that "cupola" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cupola = dome.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 DOME mean?
DOME noun- A structural element resembling the hollow upper half of a sphere; a cupola
- Anything shaped like an upset bowl, often used as a cover
- Head (uppermost part of one's body)
- Head, oral sex
- A building; a house; an edifice
- Any erection resembling the dome or cupola of a building, such as the upper part of a furnace, the vertical steam chamber on the top of a boiler, etc.
- A prism formed by planes parallel to a lateral axis which meet above in a horizontal edge, like the roof of a house; also, one of the planes of such a form
- To give a domed shape to.
- To perform fellatio on.