Stork was one of three vessels built to a 1755 design by Surveyor of the Navy William Bately, and collectively known as Alderney-class sloops in recognition of HMS Alderney which was the first to be formally contracted for construction.

This was Bately's first experience with vessel design, for which he substantially borrowed from the shape and dimensions of George II's yacht HMY Royal Caroline, built in 1750 by Master Shipwright John Hollond.

[1] Bately then added to Hollond's hull design by lengthening the "fore-rake" – the area of the bow that extended beyond the keel – in order to improve the sloop's stability in heavy swell.

[3] Carteret brought Admiralty Orders for Stork to join the Navy squadron in Jamaica and assist with defending merchant shipping from French privateers.

On 6 August 1758 she encountered Le Palmier, a French 74-gun ship of the line, off the Hispaniola coast; the outgunned British vessel was surrendered without resistance, and her crew taken prisoner.

Her Royal Navy cannons were removed and transferred to larger vessels; in their place Stork received 14 French-made 4-pounder guns, two 3-pounders and 16 antiquated pierriers à boîte for anti-personnel use.