The most common and most likely answer to this crossword clue is the 12 letter word CONSERVATORY
I've seen this crossword clue in The Times
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More clues leading to the result CONSERVATORY
- Minister to cut allowances initially pocketed by two politicians for greenhouse
- Unusual controversy about a school of music
- A politician supporting most of husband’s school of music
- Carry votes on troubled extension to home
- Almost save a politician from the hothouse
- Prisoner raves about rightwing school of music
- A controversy brewing in glasshouse
- A controversy about extension to home?
Buddy explains!

The straight part
We know that "extension to home?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extension to home? = conservatory.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 CONSERVATORY mean?
CONSERVATORY noun- That which preserves from injury.
- A storehouse.
- Having the quality of preserving from loss, decay, or injury.
- Relating to conservation.
- A large greenhouse or hothouse for the display of plants
- A glass-walled and -roofed room in a house
- A school of music or drama