Hornigold committed numerous acts of piracy during the period of peace between 1714 and 1718 when there were no enemies to attack legally. War was declared again in December 1718, so it's only after that point that he could have been licensed as a privateer. Anything he did before that point was still during peacetime when there was no (legal) excuse to attack anybody. It's unclear (to me, at least) whether Hornigold had any history of privateering before April 1714, when Lt Governor Pulleine of Bermuda named "Hornygood" as a pirate captain in the Bahamas (pirate, not privateer).

Hornigold surrendered himself to the Jamaican authorities sometime between December 1717 and February 1718 and was pardoned for his crimes. Woodes Rogers arrived in the Bahamas as governor in July 1718. Rogers is the one who sent Hornigold out hunting pirates. In the middle of September Rogers received intelligence on the whereabouts of Charles Vane. He wrote, "since I had no strenght to do better, I got a sloop fitted under the command of Capt. Hornygold to send and view them and bring me an accot. what they were". Hornigold was gone spying on Vane for three weeks, generating much anxiety for Rogers, but he came back and reported his findings. He failed to capture Vane, but he brought home a sloop whose crew had been trading illegally with the pirates. Rogers was very pleased and relieved to find out he could trust Hornigold.

In December Rogers wrote that he was optimistic about capturing more pirates because he had sent "two small cruizers mann'd with 50 men now out to look for two pirates yt. are newly sett up"--he doesn't specify if Hornigold is on one of these ships, so that will have to remain ambiguous. In January Rogers wrote, "I have paid as much as I could spare towards the bounty money H.M. has allow'd for apprehending pirates to Captains Hornigold and Cockrem [...] I hope the whole mony for a Captain, gunner, boatswain and ten pirates being taken, will be paid the gentlemen concerned [...] so as to encourage the like undertakings." These are the only references I know of to Hornigold's pirate hunting career. At this point, although war had been officially declared in Europe, it was too soon for that news to have crossed the Atlantic, so Rogers was concerning himself with capturing pirates instead of attacking national enemies.

But when we come to May 27, 1719, Rogers writes that "Yesterday one of our privateers [...] was cruizing off the Havanna"--apparently, he had now begun licensing people to privateer against the Spanish, but whether Hornigold was among that number is not explicit. So we know Hornigold had been a pirate and a pirate hunter, but whether he was ever a privateer is (to the best of MY knowledge) unsupported by evidence, but certainly within the realm of possibility. The important thing to consider is the timeline of international relations, because during times of peace there is no legal way to attack anybody who's just minding their own business, so no privateering.

Rogers describes his pirate hunters' ships rather minimally as "a sloop", "a sloop with sufficient men and arms", "two small cruizers mann'd with 50 men", and "small vessels". So who knows what any of that means. Hornigold's success as a pirate hunter depends on your perspective. He didn't get Charles Vane, whom he specifically went after, but he didn't come home empty handed either. Rogers was appreciative, and paid him for his services. So...??? Not too shabby? That'll just have to be a matter of your opinion, hehe! :)

SOURCES

Quest for Blackbeard by Baylus C. Brooks

Calendar of State Papers Colonial: America and West Indies Volumes 27-31 (multiple letters--all my quotes are pulled from letters collected here from 1714 to 1719)