The most common and most likely answer to this crossword clue is the 7 letter word SHANNON
I've seen this crossword clue in The Guardian
S
H
A
N
N
O
N
More clues leading to the result SHANNON
- Quiet girl on Irish river
- Quiet woman on river
- Quiet name adopted by nameless river
- Name borne by quiet anonymous Irish river
- Quiet touchdown at last in nameless airport
- Solo breaks soon after vacation on river
- Peace soon around new airport
- Silence soon enveloping northern river
- Irish flower girl
- 1 across being quiet in the year, forlorn ultimately
Buddy explains!

The straight part
We know that "1 across" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case 1 across = shannon.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.