3.
There may be some times of a Beagle testing limits. He may bother the cat to see how you react. If he gets too close in an aggressive way, you'll want to give the "Leave It' command and immediately give reward when he obeys.
Additionally, when cats run is the time that a Beagle will be most prone to run after them. Watch closely, so that when the cat scampers off, you can give the 'Stay' command, along with praise for doing so. Done enough times, a Beagle will learn that the cat is 'off limits'.
4. If things seem to be going well, after a week or two, you can try to have both pets eat their
food together, at the same time.
Eating a meal simultaneously tends to create a close bond with animals and over time will help establish the idea that they are both members of the same 'pack' (household). It is best to start with the cat's food still up on the counter, but with both pets called in at the same time.
5.
Until you see that the two truly get along well, continue to give each pet their own spaces to rest and play without being disturbed by the other. This is especially important for times that you will not be at home.