The most common and most likely answer to this crossword clue is the 8 letter word CARRIERS
I've seen this crossword clue in The Daily Telegraph
C
A
R
R
I
E
R
S
More clues leading to the result CARRIERS
Buddy explains!

The straight part
We know that "Naval vessels/they should be quarantined" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case naval vessels/they should be quarantined = carriers.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 CARRIERS mean?
CARRIERS noun- A person or object that carries someone or something else.
- A carrier pigeon.
- A person or company in the business of shipping freight.
- A signal such as radio, sound, or light that is modulated to transmit information.
- A mobile network operator; wireless carrier.
- A certified airline.
- That which drives or carries.
- A catalyst or other intermediary in a chemical reaction.
- A person or other organism that has a genetic trait, mutation or infection liable to cause a disease, but displays no symptoms.
- Charge carrier
- A liquid or gas used as a medium for another substance.