The most common and most likely answer to this crossword clue is the 7 letter word GARAGED
I've seen this crossword clue in Financial Times
G
A
R
A
G
E
D
Buddy explains!
The straight part
We know that "given space at home?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case given space at home? = garaged.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 GARAGED mean?
GARAGED verb- To store in a garage.
- (in combination) Having a specified kind or number of garages.