While there has been a long line of British naval vessels to bear the name Defiance, including a torpedo school ship and three United States naval vessels, there never was an HMS Defiant serving in the Royal Navy in real life. A fictional Defiant was seen in the 1962 movie H.M.S. Defiant (based on the Frank Tilsey novel Mutiny), which may have been the namesake for the Constitution-class starship.
The painting depicted a ship-of-the-line warship. Dependent on the number of guns, a ship-of-the-line was ranked from first-rate (greatest number of guns) to fourth-rate (lowest number of guns). Based on the number of gun decks visible, three in total, in the painting, the Defiant was either a first-rate or a second-rate ship. The difference between a first-rate and a second-rate could be as few as two guns (though firing lighter shot) and, without knowing more about the Defiant, it's not possible to conclusively decide the ship's rating. The six real ships named HMS Defiance that served during the 18th century were all third-rate or smaller.
The featured painting was one of two Scenic Artist Mike Okuda had created at the behest of episode writer Mike Sussman, who wanted the sailing ship, and Production Designer Herman Zimmerman who thought it apt to have it added to the starship. (40 Years of Star Trek: The Collection- auction catalog, Part two, p. 123) Both paintings were sold on 7 October 2006 in Christie's 40 Years of Star Trek: The Collection action as lot 752 for US$4,000 (4,800 including buyer's premium), having had an original estimate of US$200-300.