I don’t remember anything canonical stating that the Farragut was destroyed during the cloud creature encounter. I do remember a long-held non-canonical belief that Kirk commanded a destroyer before the Enterprise, but I can’t recall the exact source for that.
Starfleet Museum? A neat bit of worldbuilding but yea, non-canonical. Kirk is a daring Destroyer Captain in that for the Avenger/Predator page, though I don't like the designs myself, if he was on a Saladin I could see it. (Well, okay, Predator looks good if 'tos'd)
"eNew Destroyers Unleashed
The second component of the escalated resource-denial campaign was military. Unlike the earlier phase of the campaign, which had involved only defensive, surveillance, and reconnaissance activities, the post-treaty campaign involved more aggressive, even warlike, activities designed to prevent the Klingons from both obtaining mineral resources and benefitting from resources already in their possession. Most of these activities were carried out in Klingon-controlled space by Avenger and Predator destroyers. Some aspects of this military campaign can be illustrated through the actions of James T. Kirk, who before his legendary missions aboard the Constitution-class USS Enterprise (NCC-1701), was a daring and creative destroyer captain.
While at Starfleet Academy Kirk was studious and serious but occasionally showed signs of brilliance, as when he reprogrammed a simulator to allow a solution to the Kobayashi Maru exercise. However, his early years as a junior officer were uneventful and suggested, at best, a gradual rise through the ranks along with other members of his cadet class. All that changed in 2257 when Captain Garrovick, the senior officers, and half the crew of USS Farragut (Constitution class, NCC-1711) were killed in an attack by a gaseous lifeform at Tyco IV. Kirk quickly assumed command and piloted Farragut to safety at Starbase 5. Although Kirk blamed himself for the deaths, his decisive actions had attracted the attention of Starfleet Command, which began grooming him for early command of his own starship. While recuperating from injuries sustained aboard Farragut, Kirk spent 6 months at Starfleet's Advanced Tactical School on Izar. Kirk next served for 9 months as executive officer aboard the heavy cruiser USS Tav (Pyotr Velikiy class, NCC-1674) under Captain Matthew Decker. To develop his nonmilitary skills, Kirk was then sent in succession to Starfleet Intelligence in Washington, the Judge Advocate General's Office at Gravenhage (the Hague), the Federation Foreign Service Institute on Vulcan, and the Starfleet Language Academy on Cait.
In February 2260, Kirk was given the command of USS Interceptor (NCC-D243) a Predator-class destroyer assigned to Starfleet Destroyer Squadron 5 (DESRON 5) operating from the destroyer tender USS Siberia (Pachyderm class, NCC-DT22) just outside the Klingon border at Parchuk IX. Although Kirk, at age 27, was the youngest combat-ship captain in Starfleet by several years, he quickly gained the confidence of his crew through his intelligence, decisive command, and daring. For the first few months of his command, USS Interceptor served as the "wingman" of USS Snapper (NCC-D278) under the more-experienced Captain José Dominquez. Interceptor usually stood by to scan for enemy ships and protect Snapper as she went about her more dangerous work.
One mission of Federation destroyers was to maintain an extremely close watch on Klingon ships, both warships and transports, wherever they ranged in supposedly free space. Starfleet intended to clearly indicate to the Klingons that their vessels were not welcome in areas the Federation considered under their control. This shadowing led to several incidents in which Federation and Klingon ships were damaged in collisions with one another. Starfleet destroyers also boarded numerous Klingon cargo ships, passing through free space or within the newly expanded 5-ly territorial limits of the Federation, to conduct lengthy inspections on the grounds of safety or commercial regulations, transport of contraband, and even pursuit of fugitives from Federation law. Klingon ships were usually found to be in violation of obscure, rarely-enforced regulations, such as not keeping records of lifeboat drills, not possessing cargo manifests in Federation-standard English, and unsanitary food preparation areas. The ships were then towed to the nearest starbase and impounded pending payment of hefty fines or forfeiture of their cargoes. Klingon warships were, however, treated much more harshly; if they entered the 5-ly Federation exclusion zone or the territory of a Federation ally, they were immediately fired upon without prior warning.
Destroyer operations during this period have been portrayed in the popular media as "run and gun" operations in which destroyers, according to one best-selling holonovel of the time (Lone Star Ranger by Justice McMillan, Mazeppa Publishing, Rigel V, 2259), "smashed the Klingons in their ridged noses and warped home with a flock of angry Birds of Prey (sic) in hot pursuit." Such popular accounts wrongly suggest that Starfleet destroyer operations were intended to provoke Klingon responses. In fact, destroyers aimed to carry out their missions with extreme stealth and to have safely returned to Federation space before their destructive actions had occurred, much less been detected. The ideal covert operation was one that the Klingons did not realize had been carried out.
In May 2260, Interceptor was "promoted" to the lead ship of a two-ship team with USS Grenadier (NCC-D236). Kirk, often called "The Boy Wonder" because of his youth, was particularly adept at operating in hostile territory without being detected. First, he was skilled at using the interstellar terrain to travel in areas that decreased the risk of sensor contact. He would maneuver his ship through nebulae, subspace lacunae, and solar storms and hide behind asteroids and comets until he passed beyond the scanning range of hostile bases or ships. Second, he used these same hostile ships to mask his own ship's emissions. For example, he often followed in another ship's subspace wake or shadowed at a fixed distance so that his ship's sensor contact would be misinterpreted as a sensor reflection. Third, Kirk worked with his tactical officers and engineers to re-tune the resonance frequency of his warp coils to mimic those of Klingons warships and transports. Finally, Kirk also spoke fairly good Klingonese, which he used to talk his ship out of trouble on more than one occasion. (However, rumors that Kirk once talked a Klingon computer "to death" are probably untrue.)
As a rule, destroyer crews, who served in small numbers upon very fast ships, considered themselves a dashing elite. Befitting their swashbuckling image, destroyer captains were given considerable autonomy to plan and carry out missions in transborder areas. As Kirk grew more bold, he often took his ships a full sector, as much as 20 ly, past the treaty border on missions lasting several weeks. In one particularly audacious mission, he used Interceptor's speed and stealth to evade Klingon defenders near Therik G, then entered the Mosa nebula, where he waited for 3 days for a Klingon automated transport to pass by. He hid beneath this transport for 4 days, then destroyed it as it approached ak-Jom'mak shipyards at Sima IV. He tuned Interceptor's warp coil emissions to mimic those of the destroyed transport, then approached to within 200,000 km to release mines and monitoring devices that entered the shipyard and attached themselves to ships, drydocks, and maintenance vessels. After running at high speed for 4 days, Interceptor hunted targets of opportunity near the Epsilon Lalza system, destroying communications arrays, sensor stations, and M/AM refuelling depots. He next travelled within the subspace wake of a Klingon D6 cruiser for 12 days at wf 5 to take ultrashort-range sensor readings of the large fleet base at Kurrdanj II, then returned to Federation space by shadowing a D7 cruiser as it headed out for a patrol in the former TBZ."