The last we hear of Ilyn Payne is Tywin Lannister on the toilet trying to reason with Tyrion. And the last we saw of him was actually in Season 2 Episode 9, “Blackwater”, when he accompanied Cersei and the Ladies to “free them” should Stannis take the city.
Tyrion: All my life, you’ve wanted me dead.
A silence between father and son. If Tyrion’s expecting an apology, he’s not going to get one.
Tywin: But you refuse to die. I respect that. Admire it, even. You fight for what’s yours.
Tyrion says nothing, crossbow still aimed right at Tywin.
Tywin: I’d never let them execute you. Is that what you fear? You think I’d let Ilyn Payne take your head? You’re a Lannister! You’re my son.
Game of Thrones, Season 4 Episode 10, “The Children” - Official Script
This was the last we hear of him and it’s understandable as Wilko Johnson the actor who plays Ilyn was diagnosed with terminal cancer. He was then phased out of the show with his main plot going to Bronn to train with Jaime. Wilko has said in the past that he was up for a return if it was possible stating that he knows his character is still alive.
Payne is still alive in the show, and Johnson recovered from pancreatic cancer in 2014. Johnson told NME: “I’d certainly love to go back to Game Of Thrones. It was so much fun, and my character is still alive, so it’s certainly possible.”
Johnson added he received “lovely messages” from the show’s producers when he was in hospital. “There was talk about me going back,” he said.
NME, Wilko Johnson: ‘I’d love to return to Game Of Thrones’ (31/05/2916)
Since then Wilko has done a few tours so it’s possible there were scheduling conflicts if they did ever want to bring him back and just couldn’t.
I think as of Season 8 Episode 5, “The Bells”, we can assume he died in the attack on King’s Landing if he doesn’t appear in the final episode which seems unlikely.