What was the connection between increased trade in the Mediterranean and artistic output during the Renaissance?

By the early fifteenth century, trade throughout the Mediterranean had reached levels not seen since the collapse of the Roman Empire one thousand years earlier. Improvements in shipbuilding and navigation led to swifter and safer sea routes. This, combined with new mercantile connections made during the Crusades, meant that large amounts of wealth were pouring into Europe's port cities. This all led to the growth of a new merchant class, as well as the bankers that supported them.
With the influx of new capital in Europe—and Italy, in particular—the old class of nobles was no longer the only wealthy members of society. Now merchants were able to compete for prestige and power. These merchants, eager to show off their new wealth, commissioned works of art from the leading artists in their communities. Several leading merchant families in each trade city would often compete with each other to commission the greatest works of art in their community. Chief among these artistic patrons was the House of Medici of Florence, who supported nearly every type of art of the Renaissance, from painting and sculpture to music and poetry. Among the artists they supported were Michelangelo, da Vinci, and Botticelli. As patrons of the arts, they, like other wealthy families, used their position to become well-known and respected members of their cities. They used their vast wealth and popularity to gain political power in their city-states. In a sense, their support of the arts was a method for gaining further prestige and power.

The short answer is: money! 
During the Renaissance, trade by sea and land brought luxury goods to Europe, which were then sold for a profit. Hauling the thousands of pounds necessary to meet market demand was very difficult to accomplish on land. Improvements in navigation and shipbuilding enabled traders to travel much more quickly to far off places with exotic goods (like spices, silk, and precious metals) and return with hardly any increase to their burden. Once they arrived in port, the people who had commissioned the journey (wealthy merchants) or the travelers themselves would in turn sell their goods at marked-up prices. The increase in trade not only brought wealth to the Mediterranean, "stimulating" the economy-- it also provided the wealthy with enough money to invest in the arts.
Patronizing the arts was a way for wealthy individuals to "build up" or invest in their own cities, and such conspicuous consumption drove competition among the elite. With regards to religious art of the Renaissance, many of the people to have such works completed did so as a way of improving their standing with the Church or perception in society. Especially in Italy, a wealthy man might drink, gamble, and visit sex workers, but he could essentially clear his name and moral slate by paying for a very expensive piece of religious art to be created. 
https://www.britannica.com/art/Renaissance-art

https://www.encyclopedia.com/humanities/encyclopedias-almanacs-transcripts-and-maps/economy-and-trade