One thing which is a key thing that's not brought up once is his relationship with Shanks
I believe Mihawk's relationship with Shanks is the key character motivator for Mihawk.
As far as we can tell, his boredom began after Shanks lost his arm and continued to inform him joining the Shichibukai and informed his trip to going to east blue and was his motivation during the summit war
Here's how I see it. Mihawk's character arc will end when he gets over his issues with Shanks.
And if you think Mihawk doesn't have an issue with Shanks then consider the very first time thing he tells shanks in the series "I don't fight one armed has beens"... This is Mihawk's introductory line to Shanks, it's an insult about shanks' disability and his station in life... A lot of people tend to take this as Mihawk kidding around and yet there's no indication of that. Mihawk doesn't in fact fight shanks just as he says when insulting him. Even in the summit war he doesn't so obviously he wasn't kidding about that. And we learned that his boredom is in fact due to Shanks so Obviously mihawk does have as problem wth Shanks being one armed as he says when insulting him and he considers Shanks a "former" rival so the "has been" part is also serious. This was also full blown insult and this would be easily written off if Mihawk wasn't such also polite guy.
Unlike guys like Sanji who calls people "shit head" and the like casually, Mihawk insults people when he fully believes they are worth the insult. He insults Zoro's rabid attacks and insults those wimps from Impel down who try to get fresh with him. And yet he can also so change his tune when he sees something commendable like when he compliments Zoro for his tenacity or compliments Luffy for having such lofty ambitions or even Vista for being relatively famous and even Whitebeard who gets the biggest compliment Mihawk can give, which is taking him seriously in a fight. And that's the big part. Mihawk takes people seriously in fights as a compliment. He did that with Whitebeard with vista and with Zoro. There's a direct link between how seriously Mihawk takes a peperson and how much he puts into fighting them. And so that's why Him REFUSING TO EVEN DRAW HIS SWORD at shanks is a bigger indicator of Mihawk's issues with Shanks than even the direct insult he gives shanks the first they meet.
Of course though I use the word "issues" because I believe their relationship is too complicated to just be love/hate... Mihawk cared enough to seek Shanks out and ended up partying with him... then he even felt somewhat bad that he might end killing Luffy knowing how much Shanks cared about him... So like I said it's complicated but what clear is that they aren't like Luffy and Zoro with like a very solid friendship with only a few minor arguments, no... Mihawk and shanks were probably really close and now theres a massive rift between them that they both choose to ignore and just only spend time together in the little capacity they feel comfortable with... the fact that Mihawk insults Shanks and they both just change the topic of the insult immediately and proceed to hung out shows some very blatant dysfunction there
So what i think it is gonna be the full character arc for Mihawk that may or may not affect the plot is him resolving his issues with Shanks. This is by far one of the longest character conflicts in the series so I expect it to go somewhere. My guess is that the only way this can be resolved is if they fight... Not to bring this to power scaling or anything... I just mean that their friendship and the subsequent souring of the friendship all revoled around them fighting each other so I expect the resolution to come the same way.
