- "If I had obeyed my older brother earlier, we would've had the largest navy in Westeros with us as well, and our victory would've been swift."
- ―Brynden Tully
Following the Destruction of the Great Sept of Baelor, the vengeful Lady Olenna Tyrell – a Redwyne by birth, now the survivor and liege of House Tyrell – aligns herself with House Targaryen, via Varys and Ellaria Sand. When Daenerys Targaryen at last sets sail for Westeros, green-sailed ships, presumably from the Redwyne Fleet, can be seen amongst her assembled armada.
In the books
In the A Song of Ice and Fire novels, the Redwyne fleet is a fleet in the service of House Redwyne of the Arbor. It is one of the three most powerful fleets of the Seven Kingdoms, alongside the Royal Fleet and the Iron Fleet. It consists of two hundred warships, one thousand merchant carracks, wine cogs, trading galleys and whalers. According to Jaime, it is the largest fleet in Westeros.
The Season 2 Blu-ray special features display the Redwyne sigil under a list of Renly Baratheon's supporters, but in the A Song of Ice and Fire novels, House Redwyne doesn't declare for Renly. They wanted to, but during the early stages of the War of the Five Kings Queen Cersei Lannister holds the twin sons of Lord Paxter hostage at the royal court. After Renly dies, they join their Tyrell liege lords in aiding the Lannister army in the Battle of the Blackwater.
The practical result was that the Redwyne Fleet sat at anchor for much of the War of the Five Kings. It only became available to the Lannisters after the Battle of the Blackwater, but by that point Stannis's own navy was destroyed, and Robb Stark's threat was from land, not from the sea.
The addition of the Redwyne Fleet is a vital necessity to the Lannisters after the Battle of the Blackwater, during which most of the original Royal Fleet was functionally destroyed. The Lannisters consider Stannis to be a bigger threat than the ironborn, so they begin to move the Redwyne Fleet east to blockade Stannis's remaining forces at Storm's End and Dragonstone. It takes some months to move the fleet, however, and they are in no dire hurry because Stannis is in no position to attack.
Cersei worries, however, that this makes them even more reliant upon the Tyrells and their vassals from the Reach. This eventually leads her to order a new Royal Fleet – paid for entirely on credit, as the Crown is deeply in debt.
On the fourth novel, Euron Greyjoy takes advantage of the fact that the Redwyne fleet is away from the Reach, and launches a military campaign against the Reach. Once Margaery and Loras are informed that the ironborn have conquered the Shield Islands, they urge Cersei to send the Redwyne fleet back to the Reach; Cersei (who secretly gloats over the Tyrells' distress) refuses, claiming that Storm's End and Dragonstone are much more important than Shield Islands.
Loras volunteers to conquer Dragonstone and succeeds, though the victory is too costly. Then Cersei allows the Redwyne fleet to return, but in the meantime the ironborn have conquered the Arbor and its neighboring islands, using them as bases prey on shipping bound for Oldtown.
Euron and his subordinates are aware that the Redwyne fleet is on its way to fight them, and that Lord Leyton Hightower has sent against them a second fleet, but they seem unconcerned.