The most common and most likely answer to this crossword clue is the 9 letter word ADJOINING
I've seen this crossword clue in The Times
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More clues leading to the result ADJOINING
Buddy explains!

The straight part
We know that "next door" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case next door = adjoining.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.
Crossword Answer definitions
ADJOINING verb- To be in contact or connection with.
- To extend an algebraic object (e.g. a field, a ring etc.) by adding to it (an element not belonging to it) and all finite power series of (the element).
- Being in contact at some point or line; joining to