One of the reasons that I have a retriever instead of a Beagle is the breed instincts!
Yes, you do have to do tracking games with the hunting dogs to satisfy the breed instinct or they satisfy it on their own. If you can check into tracking classes with your local obedience club it will even help more and provide fun for both of you.
That said, our blacksmith has coon-hounds and he hunts. However, every time they used to go hunting he was off searching all night and half the next day for one of his prize hounds. He pays thousands of dollars for some of these dogs, so you can imagine he'll go to the end of the earth to get them back. Now with new technology they use a GPS on the collars and he only has to go halfway to the end of the earth.
As a last resort, you could get into training with a hunt trainer and learn the proper method to condition your Beagle with an E-collar. I don't recommend anyone attempt to use one of these collars for regular training and never use one without working with a hunt trainer because an accidental wrong timing of correction and your dog gets corrected for an action you want him to perform. The next thing you know you end up with a confused dog who never obeys. Go this route only after careful thought. Your clients may not appreciate the collar on one of your dogs. People who do not hunt their dogs often find the collar offensive and some people think they are cruel. Plus you could do your dog more harm than good if you are properly supervised and trained first.
Remember the first rule of dog training. Never issue a command you can't enforce. Until you can trust the Beagle in a fenced area to respond to every command on leash, then off leash, keep it on a long lead.
Good luck.
He shall be everything humanity strives to be: Honest, Loyal, Kind in Heart, and Strong in Spirit. Therefore, you shall call him Partner and Best Friend."
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