Will Adar Be Back in The Rings of Power Season 2?
The short answer: he certainly will.
As for the long answer, Adar is still alive at the end of Season 1.
There is an unfinished business between him and Sauron – as Episode 6 demonstrated, Adar even believes that he had managed to kill Sauron. But, of course, Sauron, being a fallen angel, is not so easy to dispatch.
Now he's back, after revealing that he was wearing the guise of Halbrand throughout Season 1, and in the final moments of the season's final episode he is shown to be returning to the freshly devastated Mordor.
From the hints we were given, it is quite likely that the eruption of Mount Doom and making of Mordor were originally conceived by Sauron, and Adar has played into Sauron's hand unwittingly. But now it is time for the Dark Lord himself to take the stage.
Accordingly, Season 2 is likely to explore this dynamic between them. And by "dynamic" we mean "struggle".
Sauron is going to establish himself as the ruler of Mordor and the true master of orcs, somehow. But given what we have seen of Adar, he's not going to meekly let Sauron take over.
Not only because evil warlords are usually not big of stepping down from their positions willingly – Adar just really hates Sauron, to the point when mere mention of Sauron's name angers him.
You see, Adar is actually a first-generation orc, meaning he was one of the elves captured and corrupted by Morgoth at time when Sauron was Morgoth's chief lieutenant. Not only this could not engender any warm feelings towards Sauron in him, over time he came to regard "normal" orcs as his children.
Even his name is an elven word for "Father". And he turned on Sauron in the past, because of brutal experiments Sauron was doing to the orcs.
By the end of Season 1, though, Adar appears to have support and loyalty of all the orcs in Mordor, while Sauron appears to be alone, and still not much more powerful than a mortal man.
Certainly, he can do a few cool magic tricks, but so far he had shown nothing that could make a crowd of angry orcs submit. Hopefully, the showrunners would make him come up with a cunning plan for overthrowing Adar.