The most common and most likely answer to this crossword clue is the 6 letter word ANNEXE
I've seen this crossword clue in The Guardian
A
N
N
E
X
E
More clues leading to the result ANNEXE
- Former partner taken back by woman in part of house
- Extension built by woman overlooking river
- Queen cross over East wing
- Woman houses old lover in extension
- Queen by eastern extension
- A file containing news supplement
- Join by contributing to A Year in Provence
- Princess rejecting old flame in addition
- Pick up one old lover for bit on the side?
- A letter marking the spot, we hear, for extension
Buddy explains!

The straight part
We know that "extension" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extension = annexe.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 ANNEXE mean?
ANNEXE noun- An addition, an extension.
- An appendix to a book or document.
- An addition or extension to a building.
- An addition to the territory of a country or state, from a neighbouring country or state, normally by military force.
- Alternative spelling of annex