This is probably controversial but Klaus never really had a redemption arc.
He never actually changed in all five seasons of the originals. The only thing different about him between when he is first introduced in tvd to originals is that we see more of his relationships. Yes, he loved Camille. Yes, he loves Hope more than anything. But did his behavior change? No.
"well he died for Hope!" shut up. That was literally the most selfish thing he could've possibly done at the time. Her mother had literally just died and Elijah offered to do it. Elijah had nothing left to live for. Hayley was dead and he blamed himself for it. His relationship with Hope was never going to be the same. His relationship was never even going to be the same with his siblings so he was done. Elijah wanted to die. Klaus should've let him. Instead Klaus chose the easy way out. Instead of being a parent to Hope he ran. He killed himself when she needed him most.
Let's also talk about the face that from s1 to s5 he was just as brutal as ever. He did insane things in all the seasons.
Season 1 he comes back to New Orleans and wants the city back. Why? Because he's Klaus Mikaelson that's why and he feels entitled to everything he wants. Not to mention the way he uses Cami in the first season. I love Klamille but still. He compelled her, made her think she was crazy, and quite literally made her bait for Marcel.
Season 2 he was still bad. Yes, he had some good moments but his over arching character remained the same. What he did with Dahlia and his "punishments" for his siblings for daggering him were insane. He murdered yet another one of Elijah's lovers in front of him. Ripped Hayley from their child. He constantly was claiming Hope was his child and seemed to conveniently forget she had a mother too. And instead of telling his siblings his plan he still is just as paranoid as ever and refuses to trust them. Does that sound like a man who's really had character devlopment?
Season 3 he is marginally better. But I am a firm believer that the writers didn't know how to give him a real redemption arc, so they just made the characters around him do things that were just as bad as him to make him look better. Especially Elijah. Freya too.
Season 4 he attempts to be a dad for the five seconds he has. But then he's forced away from Hope. Again. Which is horrible. But he's only being forced away from her physically. He has a phone. He has a daughter who quite literally can astral project to see him whenever she wants. And while he's away what does he do? Goes on a murder spree.
"He was protecting Elijah? Like he said he wouldn't know any enemy if they sat down at his piano!"
What were these so-called enemies going to do to Elijah? He was still an original even without his memories. It's not like anyone had white oak to kill Elijah, so why was Klaus so worried? Honestly it was just an excuse for his behavior, which he always had one.
Then Hope sees him being killing someone on accident. What does he do? Does he do the mature thing, like a parent should and apologize? No. Instead he cuts off contact with his child and never speaks to her again! Until she kidnaps her mother to get his attention because she misses her dad. That sounds like a man who deserves father of the year! And that definitely sounds like someone who grew up from when we first saw him... yeah, right.
And again, instead of being with her after her mother dies when she needs him most, he kills himself. He takes the easy way out and runs from being a parent again and again.
So yeah, I don't think Klaus changed as much as people like to say he did. And he wasn't a good dad, even if he was a loving one.