The most common and most likely answer to this crossword clue is the 5 letter word FLEET
I've seen this crossword clue in The Times
F
L
E
E
T
Buddy explains!

The straight part
We know that "Navy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case navy = fleet.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 FLEET mean?
FLEET noun- A group of vessels or vehicles.
- Any group of associated items.
- A large, coordinated group of people.
- A number of vessels in company, especially war vessels; also, the collective naval force of a country, etc.
- (British Royal Navy) Any command of vessels exceeding a squadron in size, or a rear admiral's command, composed of five sail-of-the-line, with any number of smaller vessels.
- An arm of the sea; a run of water, such as an inlet or a creek.
- A location, as on a navigable river, where barges are secured.
- To float.
- To pass over rapidly; to skim the surface of.
- To hasten over; to cause to pass away lightly, or in mirth and joy.
- To flee, to escape, to speed away.
- To evanesce, disappear, die out.
- To move up a rope, so as to haul to more advantage; especially to draw apart the blocks of a tackle.
- (of people) To move or change in position.
- To shift the position of dead-eyes when the shrouds are become too long.
- To cause to slip down the barrel of a capstan or windlass, as a rope or chain.
- To take the cream from; to skim.
- Swift in motion; light and quick in going from place to place.
- Light; superficially thin; not penetrating deep, as soil.
- Floor; bottom; lower surface.
- A house; home.