What's west of Westeros
What is west of the sunset sea?
The show and books are on two different continuities, so the answers may be different for both.
@Shevliaskovic's answer gives a good quote from GRRM about how dangerous it is to cross the sunset sea and even states that no one has ever successfully crossed it.
Is there a trade between Westeros and Asshai over the Sunset Sea or are these unknown waters?
Over the = sunset = sea? No . Nobody has ever crossed the sunset sea to find out what is on the other side.
Merchant ships to Asshai sail east through the Summer Sea and the Jade Sea, which are connected by the straight line at Qarth.
The citadel, so Martin spoke
We know of an example where someone tried to cross the sunset sea in the past. Brandon the shipbuilder who tried but was never seen again. That event then resulted in Brandon the Brenner setting fire to his father's ships and ending the power of the North at sea.
"Do you remember your story, Bran?" said the maester as they left. "Tell Osha who they were and what they did if you can."
He looked at the passing faces and the stories came back to him. The maester had told him the stories, and Old Nan had brought them to life. "... Theon Stark is the really thin one with the long hair and the thin beard. They called him the 'hungry wolf' because he was always at war. This is a Brandon, the tall one with the dreamy face, he was Brandon the shipbuilder because he loved the sea. His grave is empty. He tried to sail west across the sunset sea and was never seen again. His son was Brandon the Brenner for laying the torch on all of his father's ships in mourning for Rodrik Stark, who won Bear Island in a wrestling match and gave it to the Mormonts. And that's Torrhen Stark, the king who knelt. He was the last king in the north and the first lord of Winterfell after giving in to Aegon the Conqueror. ... "
A Game of Thrones, Bran VII
Lord Gylbert seems to believe that there are lands beyond the Sunset Sea, although this could just be that he suspects, is rooted in stories, or even comes to him from a dream.
Lord Gylbert began to speak. He told of a wondrous land on the other side of the sunset sea, a land without winter or want, in which death had no rule. "Make me your king and I will lead you there," he shouted. "We will build ten thousand ships like Nymeria once did and sail with all our people to the land beyond the sunset. There every man should be a king and every woman a queen."
Aeron saw that his eyes were gray now, blue now, and as changeable as the seas. Crazy eyes, he thought, fool eyes. The vision he spoke of was undoubtedly a noose the storm god had set to lure the ironborn to destruction.
A feast for crows, the drowned
The Ironborn themselves seem to believe that there is something beyond the Sunset Sea, but the Maesters believe that this is pure speculation.
Among the Iron Born, the first of the first men to come to the Iron Islands is believed to have found the famous Seastone chair in Old Wyk, but the islands were uninhabited. If so, the type and origin of the chair makers are a mystery. Maester Kirth has suggested in his collection of iron-born legends, Songs the Drowned Men Sing, that the chair was abandoned by visitors from the Sunset Sea, but there is no evidence, only speculation.
The World of Ice and Fire, Ancient History: The Age of Dawn
However, Archmaster Haereg once believed the Seastone chair had come from the Sunset Sea before dismissing the idea as pure speculation.
Archmaester Haereg once put forward the interesting idea that the ancestors of the Ironborn came from an unknown land west of the Sunset Sea, and quoted the legend of the Seastone chair. The Greyjoys' throne, carved from an oily black stone in the shape of an octopus, is believed to have been found by the First Men when they first came to Old Wyk. Haereg argued that the chair was a product of the islands' earliest inhabitants, and it wasn't until the later stories of Maesters and Septons began to claim that they were indeed descended from the First Men. But this is pure speculation, and in the end Haereg himself rejected the idea, and we have to.
The world of ice and fire, the iron islands
The maesters themselves even admit they don't know anything about what lies beyond the sunset sea.
Unfortunately, the farther we are from the lands that the men of the east call the Sunset Kingdoms, the more and more knowledge of the Citadel becomes, for the congress with the more distant areas of Essos has ever been sparse. We know even less about the southern foothills of Sothoryos and distant Ulthos, and in general nothing about the lands that could be beyond the last light and above the sunset sea.
The world of ice and fire, other countries
The only cannon cards we have are those in the lands of ice and fire, and as far as I can tell, these do not contain anything beyond the sunset sea.
There are various sources claiming that the Iron Islands ruled the Sunset Sea for centuries and used it to tour certain parts of Westeros. including Euron Greyjoy. However, it seems to me that these springs only mean the parts of the sea that are close to Westeros and not that they delved too deeply into them.
I couldn't find any information on what is west of the Sunset Sea on the show. However, I did find an article by Elio that covers the image in your question. Unfortunately, he doesn't go into detail about what's in the west.
Best of all, the article is heavily illustrated with concept art and high-resolution still images from the sequence. The highest view of the map with Essos ... including the east coast of Essos on the opposite side of the Sunset Sea.
Game of Thrones, Art of the Title Interview
Beyond that, there doesn't seem to be anything on the show about the West.
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