Here is what you can expect with the typical Beagle:
Young puppy 2 to 4 months: Moderately hyper. Everything is new. Focus is poor. He'll jump from one thing to the next without much thought. He can do okay without extended outdoor play; however, that will end very soon.
Puppy 4 months to 12 months: Very hyper. This is the stage where you will see the most hyper behavior; though, without proper methods to vent, even adults can be this way. Beagles that are not given ways to release pent up energy can become very frustrated and even frenzied.
12 to 18 - 24 months: A turning point, moderately hyper. This is when owners most often question if their Beagle is acting normal. He has the body of an adult (or just about) but still has puppy-like tendencies that make him want to play every second, demand attention from you and generally have trouble just chilling out. It is at this point that the emotional needs to catch up to the physical. Not to worry, as long as he's receiving what he needs, he will indeed calm down.
24 months +: Somewhat hyper, but controlled. At the age of 2, and especially by 2.5 years old, things will change. Both his body and his mind are that of an adult. By now you know your Beagle, he has a good routine of both exercise and rest. He has plenty of toys to keep himself occupied and he often mimics the vibe of the household. If everyone is relaxing, he will too. If people are busy and things are going on, he wants to join in on the fun. This said, adult Beagles can find life to be frustrating if their true needs are not met.
8+ years: Slightly to not at all hyper. The senior Beagle has seen it all, smelled it all and is satisfied that he's run, explored and taken in the world. As these senior years go by, a Beagle will enjoy the familiar and not need to see what else is out there. He's happy relaxing near you, or alone in his area. To slow the loss of muscle mass and keep the heart strong, do continue to take him for walks, albeit at a slower pace than his younger counterpart.