He may have replaced Sun Ben as Yuan Shu's Inspector of Yu, since Sun Ben was serving as Grand Commandant of Danyang at that point. However, this seems unlikely, given the details of the SGZ's account.
Then, Guo Gong, Inspector of Yuzhou, arrived beneath the city gates with some tens of thousands of men. Some said that he was one of Lü Bu’s accomplices, and all were in fear. Guo Gong asked for an audience with Xun Yu. Xun Yu was about to go out to meet him, but Xiahou Dun and others said, “Sir, you are in charge of this whole province. Should you go, your life would be endangered. Do not go.” Xun Yu replied, “Guo Gong has not been a close friend with Zhang Miao and the others. By his coming so speedily, he must not have decided on a plan of action yet. If I go talk to him before his mind is set, even if he doesn’t take in my words, at most he would stand neutral. However, if we doubt him right at the start, he might come up with a plan against us in anger.” Guo Gong, seeing that Xun Yu had no trace of fear, thought that Juancheng must be difficult to conquer. Therefore, he led his men and left.
Given the history of violence between Cao Cao's army and Yuan Shu's, it seems implausible that one of Yuan Shu's highest-ranking men would be able to bring an army into Yan and request an audience with Xun Yu. Since Guo Gong was opportunistic, rather than immediately hostile, I believe it is safe to say that he was not Yuan Shu's affiliate.
There are limited other options. Tao Qian tried to claim Yu, but while Guo Gong's appointment predates Liu Bei's, it is even less likely that one of Tao Qian's men could have requested such an audience, as Cao Cao and Tao Qian were actively at war at that very moment. And Tao QIan's territory in Yu never really extended west of Pei in any case. While a Pei-based Inspector of Yu could theoretical have made his way to Jiyin, the open hostilities between Cao Cao and Tao Qian render it unlikely.
Yuan Shao tried to insert his own Inspector of Yu in 191, though his man was driven out by Sun Jian and Yuan Shu. I haven't found any evidence to suggest that Yuan Shao attempted such a thing again, so it seems unlikely that Guo Gong could have been one of his subordinates. And given that Cao Cao was acting as Yuan Shao's subordinate at the time, Guo Gong's opportunistic views on the situation make affiliation with Cao Cao's nominal overlord unlikely.
Though Liu Biao held extensive territory along Yu's southwest border (namely the commanderies of Nanyang and Jiangxia), he never had a history of appointing subordinate Inspectors to other provinces, so it is improbable that Guo Gong was associated with him.
Li Jue's regime is, to my mind, the most likely answer. Based in Sili, Li Jue did still extend some influence into Yu province and would certainly have had reason to attempt to establish his own man in the area. Li Jue and Cao Cao had a strained relationship, with Li Jue recognizing Cao Cao's rule over Yan while remaining uncertain towards him. Given their history, Guo Gong's opportunistic intentions seem quite appropriate. And given that Zhang Miao was based in Chenliu and Lü Bu entered Yan from Henei, an affiliate of Li Jue's regime would have ample time to learn about these movements and react to them. So personally, I think it is most likely that Guo Gong was appointed by Li Jue's regime.
As for the size of his army, it seems impossible that any of the candidates for his overlord could have fielded tens of thousands of men in Yu province. None of them had that kind of control over the region, especially after Cao Cao's thorough defeat of Yuan Shu in the previous year. Most likely, the size of Guo Gong's army is exaggerated to flatter Xun Yu.