New dog harasses older cat

2 weeks ago we got an 11,5mo poodle that just felt at home right away, overall a really sweet boy, we also have a 2,5yo maine coone that is often afraid of anything or anyone new. The first week our animals were separated almost all of the time. When we started to introduce them to each other a week ago they behaved mostly fine, pretty much ignored each other and occasionally tried to sniff each other. Now they can be in the same room no worries, they may both lay on the floor in relaxed positions, can lay or sleep on the same bed, just not together. The only issue we had is when our dog is chilling and chewing on its bone he would growl on the cat if he was simply passing by. Sometimes the dog would chase our cat for a bit, the cat might rarely hiss, he never actually attacked the cat tho. But yesterday when he chased him again he came back with some of the cat's hair in his mouth. What can we do to prevent such behaviours on the dog's part? We would be super fine with them just ignoring each other if they can't be friends.