The most common and most likely answer to this crossword clue is the 11 letter word DOMESTICITY
I've seen this crossword clue in The Times
D
O
M
E
S
T
I
C
I
T
Y
Buddy explains!

The straight part
We know that "Feeling of home" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case feeling of home = domesticity.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 DOMESTICITY mean?
DOMESTICITY noun- Life at home with one's family.
- (plural) Domestic chores; housework.
- Affection for the home and its material comforts.