He’s a 4 year old Arab. That says it all. Some horses are hot. Every hot horse I have ever owned has been that way until the day they died of old age. DO NOT get caught up on the myth that feeding him, or giving grain or other concentrates are going to make him hot. The only truth to this is that if you don’t feed him enough he will have less energy, just like if you had poor nutrition you’d have less energy. You just need to learn how to handle him. hot horses can be a lot of fun, but it will take a lot more than some lungeing and turnout to calm him down. I used to cometitive trail ride my arabs and they were perfect for that…. 30 miles of nothing but trotting and cantering…they learn to pace themselves.
Just remember 4 year old Arabs are not for everyone. Arabs in general are not for everyone. As he gets older and you work with him more he will become more attentive, better behaved, easier for you to work with, but he will probably always be hot. You not liking his his personality though is your problem, not his, and pumping him full of calming supplements, cutting his feed, etc is not the solution. He needs a job.