After the death of the Ancient One, Mordo believes that her abuse of the dark dimensions led to her betrayal as a consequence of interfering with the laws of nature. If Mordo had his way, Strange wouldn't have given up the time stone, and the snap/Thanos' victory would have been permanent. Wanda Maximoff was the film's main villain, trying to use the Darkhold to kill and steal America Chavez's multiverse traveling powers so that she could return to Tommy.
To Strange's astonishment, Mordo hugs him and greets the duo with kindness, but to their disappointment, Mordo inevitably drugs them, turning Strange over to the Illuminati for judgement. Strange is able to get Mordo to come with him to fight Dormammu, but when Strange uses the time stone to reverse Kaecilius' victory and deceive Dormammu into capitulating, Mordo draws the line and declares he'll no longer serve Kamar-Taj
The seeds of the conflict with Mordo were sown by Strange when he told Mordo that the Ancient One had been drawing off the dark dimensions to stay alive.
If Strange is able to help Mordo keep his demons in check, he could return to the mystic arts.
One of the biggest questions going into Doctor Strange in the Multiverse of Madness was who would be the main villain to Stephen Strange. Mordo stated that he wasn't perfect when he came, but she gave him the power to overcome his desire and defeat his demons. Mordo is likely to be one of Strange's greatest adversaries after he tampered with the book in the film.
The Ancient One told Strange that he needed Mordo's strength just as Stephen needed Mordo's flexibility to serve the greater good.
Mordo is a crucial ally to Strange, helping him use his sling ring and training him for combat.
Mordo was the one who convinced the Ancient One to let Strange back in. It was thought that Karl Mordo would be the main villain in Multiverse of Madness after he swore to rid the world of sorcerers who abuse their power at the end of Doctor Strange. Mordo is concerned for Strange when the Ancient One abandons him on Mount Everest to motivate him to open a portal for the first time.
Hopefully the sparing of Earth-616's Mordo means he will serve as a greater antagonist in the coming Doctor Strange films and audiences will finally get that on-screen confrontation between him and Earth-616's Strange. He's still faithful to the mystic arts, even though he might have played a role in Earth-838's Strange being executed. At the end of WandaVision, it was suggested that Wanda might fall for the temptations of the Darkhold, as she embraced her worst impulses.
Mordo and Strange's relationship begins when Strange tries to get Kamar-Taj to heal his hands the same way that Jonathan Pangborn healed his spine. Mordo would be an important ally in protecting the multiverse with Wong and Strange. In the film's final end credit scene, Mordo takes back Jonathan Pangborn's power to heal his spine and says the biggest problem is that there are too many sorcerers.
Multiverse of Madness was supposed to open with a deleted scene in which Mordo kills Wanda for abusing magic in Westview. Mordo believes that by interfering with nature's laws, the consequences will eventually catch up and destroy the reality they've been trying to protect. Mordo brought Strange to Kamar-Taj to meet the Ancient One, but he was kicked out after Strange disrespected their practices. Mordo says it's important to trust your teacher and not lose your way when Strange asks why he would follow someone he knows nothing about.