It does have a fleet on the Shield Islands:
The most telling blow was struck by King Garth VII, the Goldenhand, King of the Reach, when he drove the ironmen from the Misty Islands, renamed them the Shield Islands, and resettled them with his own fiercest warriors and finest seamen to defend the mouth of the Mander…
Soon after, he turned his attention to the sea and drove the last ironmen from their strongholds on the Shield Islands. Thereafter he resettled the islands with his fiercest fighters, granting them special dispensations for the purpose of turning them into a first defense against the ironborn, should they return. This proved a great success, and to this day the men of the Four Shields pride themselves on defending the mouth of the Mander and the heart of the Reach against any and all seaborne foes…
Most seagoing vessels dared not sail beyond Highgarden, but longships with their shallow draughts could navigate as far upstream as Bitterbridge. In ancient days, the ironborn had boldly sailed the river road and plundered all along the Mander and its vassal streams … until the kings of the green hand had armed the fisherfolk on the four small islands off the Mander’s mouth and named them his shields.
Two thousand years had passed, but in the watchtowers along their craggy shores, greybeards still kept the ancient vigil…Warhorns would echo across the waters, from Greenshield and Greyshield, Oakenshield and Southshield, and their longships would come sliding out from moss-covered stone pens along the shores, oars flashing as they swarmed across the straits to seal the Mander and hound and harry the raiders upriver to their doom.
They’re longships rather than galleys, but there’s 50 or more of them. Perhaps not enough to take on the Iron Fleet, although they did a fine job against Quellon Greyjoy, but enough to slow it down and allow the Redwyne Fleet to mobilize…if Euron hadn’t tricked them.