The most common and most likely answer to this crossword clue is the 9 letter word COMPOSURE
I've seen this crossword clue in The Guardian
C
O
M
P
O
S
U
R
E
More clues leading to the result COMPOSURE
- Calm old representative retained by firm? Yes
- Army rations needing certain self-control
- School has nothing certain to provide tranquillity
- Nothing in school guaranteed calmness
- Tranquillity of old city shown in design
- Company representative certain about nothing, but shows aplomb
- Self-control in contest with old firm
- Clegg’s friend certain to show calmness
- Poise of business representative certain about love
- Write about ancient city’s tranquillity
Buddy explains!

The straight part
We know that "tranquillity" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case tranquillity = composure.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 COMPOSURE mean?
COMPOSURE noun- Calmness of mind or matter, self-possession.
- The act of composing, or that which is composed; a composition.
- Orderly adjustment; disposition.
- Frame; make; temperament.
- A combination; a union; a bond.