The most common and most likely answer to this crossword clue is the 9 plus 1 letter word TROOPERS} –
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Buddy explains!

The straight part
We know that "Swearing 19 Downs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case swearing 19 downs = troopers} –.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 TROOPERS} – mean?
TROOPERS} – noun- A soldier of private rank in cavalry or armour.
- A cavalry horse; charger.
- A soldier.
- A troopship.
- A state trooper.
- A mounted policeman.
- One who endures adversity or hardship with an attitude of stoicism and persistence.
- To work as a trooper.
- To work steadily at an unpleasant job without complaint.