Please remember that this is a theory. It's simply my opinion, not fact, and shouldn't be treated or regarded as such.
Well, since no one has used this board, guess I'll be the one to post the first theory-related thread. As we all know, Potential Released has the ability to unlock the latent power in a being to the point where their base state receives an exponential increase in power. Gohan is the most prominent (and the only) example of this, to which his base state is superior to the Super Saiyan 3 transformation. However, did you ever notice how Gohan's Potential Released is very similar to Gokū and Vegeta's base states after mastery of godly ki? (Similarities being: exponential increase in power without transforming, and the same white-colored aura)
In the manga, Old Kaiōshin claimed that he was sealed because the one that sealed him (later revealed to be Lord Beerus) feared his ability to increase the power of a normal being. My theory is, given that Old Kaiōshin is a deity himself, I think his ability is that he infuses a certain amount of godly ki (though not as much as a God has) to amplify the normal ki of anyone he chooses.
Elaboration: In terms of using godly ki to amplify normal ki (while still being predominantly normal ki), we've already seen this before. Twice in fact. The first instance, after Gokū lost the Super Saiyan God transformation, it was stated that he still retained its power, despite it just being normal ki at that point (proven by the Dragon Team's ability to sense his ki). The experience of having godly ki amplified his normal ki, to the point were he could surpass the Super Saiyan God transformation.
This leads into the second instance, when Gokū fought Freeza for the second time. After Freeza went into his final form, Gokū also powered up with just his normal ki. At this point in time, Freeza in his first form was stronger than Tenshinhan, Piccolo, Kuririn, Jaco and even Gohan, after the half-Saiyan went ultimate and Super Saiyan, so it was clear Freeza was much more powerful than a Super Saiyan 3 in his final form. Considering Gokū was stronger than that with just his base state, this was due to his experience with godly energy.
Considering that Whis (who has the ki of a God, stated by the Oracle Fish) and his training methods also gave Vegeta the ability to obtain and sense godly ki, I don't think it's far-fetched that Old Kaiōshin gave Gohan a little bit of godly ki as well. Though, like Gokū after the Super Saiyan God transformation and before transforming into a Super Saiyan God Super Saiyan, it's still just normal ki for Gohan, amplified by godly ki.
Possible objections/counterarguments:
But if Gohan has godly ki like you said, how come he didn't transform into a SSGSS when he transformed into a SS after going ultimate in G&G and RoF?
Well, first of all, I did say that it's primarily his normal ki, just amplified by godly ki. We've seen this before. And not to mention, Gokū was also still just a regular Super Saiyan with the power of a Super Saiyan God when facing Beerus, and his hair wasn't blue either.
So are you saying that Gohan when he goes ultimate is on the same level as Gokū and Vegeta?
Not quite. Gohan didn't obtain as much godly ki as they did. Gokū has flat-out transformed into a full-fledged God, to the point where his ki couldn't be sensed, so Gokū obviously had experience with a lot of godly ki. Vegeta trained with Whis in order for his godly ki to develop to the point where both he and Gokū can become full-fledged Gods again by going Super Saiyan God Super Saiyan. And no, Gohan is not a god like Gokū and Vegeta can transform into.
If Gohan has godly ki, then why can't he sense it too?Most likely because he hasn't trained much with it. Again, Gohan's ki when going ultimate is still primarily normal ki, it just receives a boost from the godly ki that Old Kaiōshin gave to him. We've seen this boost to normal ki twice with Gokū and once with Vegeta. And not to mention, it even took Vegeta a while to sense godly ki, given that the Oracle Fish in Super episode 18 said "Ah, so you're finally able to sense the ki of a God, huh?" This statement indicates that while Vegeta received the power boost like Gokū sensed from him, it took Vegeta some time to be able to sense godly ki. So, the same can apply to Gohan, he just needs training (with Whis, specifically).
So you're saying it's possible for Gohan to get stronger and eventually become a Super Saiyan God Super Saiyan if he trains with Whis too?Get stronger? But of course! Vegeta only had normal ki, and ended up getting godly ki and becoming a Super Saiyan God Super Saiyan too (Hell, Freeza got freaky strong freaky fast somehow). If Gohan has a small amount of godly energy, he surely can too by training with Whis. And not to mention, the Nameless Nameccian (aka God, since he lacks a name) became a God from training with the previous God of Earth. So again, I don't think it's far-fetched that a God can give godly ki to a non-god. After all, we've seen it with the Nameless Nameccian long before and with Vegeta very recently, and I think Old Kaiōshin did so too with Gohan. Hence, why Old Kaiōshin was so adamant about Beerus allegedly "fearing his ability". I'm sure Beerus wouldn't want mortals with godly energy "gunning for the job of destroyer" right?
TL;DR: I theorize that Gohan's Potential Released is more or less the same as Gokū and Vegeta's base state after mastering godly energy, just not on time same level in terms of power. We've seen that gods can give non-gods godly ki with Whis and Vegeta, so I speculate that Old Kaiōshin did the same with Gohan. Gohan just needs training with Whis to get to that level Gokū and Vegeta are on.
Please remember that this is a theory. It's simply my opinion, not fact, and shouldn't be treated or regarded as such.