The President's Agent is a one-man agency working for the U.S. President.
It is not on the books. It has been around, apparently, for quite a long time and it is still a very well kept secret. Understandable since if its existence was made known, the hoopla over the constitutionality of it would be tremendous, not to mention hand-wringing over the ethics of have one person given the kind of authority and power that is entrusted to the person designated as the President's Agent.
By tradition and likely for some very good reason there is only one agent at a time. There does not appear to be any particular stepping stone to becoming that agent since those few we know about came from different backgrounds. The ones we know about were all something different before being tapped to take over the role. The main criteria is that the individual has to be able to work alone and in quiet and get the job done or die trying. Preferably the former.
Should the agent last long enough to decide to retire, the promise is made for a very comfortable next career, using the tremendous influence of the Oval Office to reward that agent for his service. The number of agents who have lived to enjoy it, though, is very low. The jobs that the President's Agent get are those the other Intelligence agencies either couldn't or wouldn't handle which means they were next to impossible from the beginning.
The time period covered by the recorded adventures span almost one hundred years, going back to the end of WWII and the Manhattan Project, up to just a couple years into the current future, and then nearly two decades from now.