I'm guessing that you're asking about the meaning of "up" in these phrases.
In English, we talk about going "up north" and "down south", so we often say that people, "live up in the North of England", though it would be equally correct to say, "live in the North of England."
To "chase something up" is not the same as "chase after something". To chase means to pursue, but to "chase up" means to find out what has happened to something. For example if someone hasn't done something they promised to do, you might say, "I'll chase it up" meaning you will find out why they haven't done it.