The most common and most likely answer to this crossword clue is the 6 letter word STOREY
I've seen this crossword clue in The Sunday Telegraph
S
T
O
R
E
Y
More clues leading to the result STOREY
- Floor, from which relation picked up?
- Larder with unknown level
- Level on a building plot, we hear?
- Extremely sexy nurses rent floor of building
- Narrative including header in equaliser, getting level
- Eastern mines lie level
- Floor of yard behind shop
- Level enclosure filled with mineral
- Co-ordinate on shop floor
- Fabrication’s sound for part of house
Buddy explains!

The straight part
We know that "part of house" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of house = storey.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 STOREY mean?
STOREY noun- A building; an edifice.
- A floor or level of a building or ship.
- A vertical level in certain letters, such as a and g.