I was looking at the Time Lord Wiki which told me some helpful information but it didn't really say what your average Time Lord or Time Lady actually does. We mainly get the perspective of the most renegade Time Lord ever the Doctor but he doesn't act like the others. This is a large race of people and one of the oldest. So what does a Time Lord do?
Side note: The TARDIS that the Doctor drives is said in one episode that it actually requires 6 Time Lords to operate it correctly. This doesn't mean that every TARDIS requires this and it also doesn't mean that it's true due to rule #1 but it does suggest that Time Lords are meant to travel together. Which means that they have a society where they do or once did travel through time and space together so they don't just sit on Galifrey twiddling their thumbs until the Doctor or Master stir things up.