The most common and most likely answer to this crossword clue is the 8 letter word SERENITY
I've seen this crossword clue in The Sunday Telegraph
S
E
R
E
N
I
T
Y
More clues leading to the result SERENITY
Buddy explains!

The straight part
We know that "feeling of calmness" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case feeling of calmness = serenity.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 SERENITY mean?
SERENITY noun- The state of being serene; calmness; peacefulness.
- A lack of agitation or disturbance.
- A title given to a reigning prince or similar dignitary.