The most common and most likely answer to this crossword clue is the 6 letter word MEDICI
I've seen this crossword clue in The Guardian
M
E
D
I
C
I
More clues leading to the result MEDICI
- Italian family by the sea here in Cannes
- Doctor and I in an old Italian house
- Person who treats one powerful family
- One last doctor in a political dynasty
- Old family doctor heading for Ipswich
- Riviera location here in France, and house in Florence
- Famous family producing two-thirds of pharmaceutical products
- Bones associated with Italy’s foremost Renaissance family
- Student doctor with independent family from Italy
- Italian house loses last three drugs
Buddy explains!

The straight part
We know that "an old Italian house" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case an old italian house = medici.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.