chase someone or something up
to seek someone or something out; to look high and low for someone or something. I will chase Tom up for you. I will try to chase up a buyer for your car.
chase someone or something up something
to drive someone or an animal up something, such as a tree, a hill, a cliff, etc. The ranchers chased the mountain lion up a tree. The bull chased the rodeo clown up into the stands.