Two different answers: your cat, and cats outside
Inside the home, most Beagles can learn that a specific cat belongs to the household and is not to be chased. Beagles are pack-minded and generally peaceable, and a confident indoor cat that stands its ground often earns a hound's respect quickly. Puppies raised with cats usually settle fastest, but many adult Beagles with no cat history also adapt when introductions are unhurried and the cat always has the choice to leave.
Outside, the calculation changes completely. A running cat across a garden or street activates the chase sequence that scent hounds were bred for, and even a Beagle that sleeps beside its own cat may pursue a stranger's cat with total focus. Leads, secure fencing, and a check before opening doors are permanent habits in a Beagle and cat neighbourhood, not temporary precautions.
Staging the introduction so both animals cope
Begin with separation and scent. Keep the cat and Beagle in different areas, swap bedding between them, and feed both near the closed door so each associates the other's smell with good things. After several calm days, allow visual contact through a baby gate or glass door, rewarding the Beagle for glancing at the cat and then back at you. Short sessions, ended before excitement climbs, teach more than one long tense meeting.
First shared-room time should happen with the Beagle on a lead and harness, the cat free to leave, and high perches or a cat door to a safe room in place. Let the cat set the distance. If the Beagle fixates, trembles with excitement, or cannot take food, you have moved too fast - return to barrier work for a few more days rather than pushing through, because rehearsed chasing is hard to undo.
Designing a home both species can relax in
Cats need vertical territory a Beagle cannot reach: shelves, tall scratchers, and the tops of wardrobes become the cat's highway above a nose-driven dog. Litter trays and cat food must sit where the Beagle cannot raid them, because a Beagle will eat both cat food and litter contents with enthusiasm, to the cat's stress and the dog's detriment. A stair gate that cats slip through and Beagles cannot gives the cat a whole dog-free floor, which dramatically lowers daily tension for both.
Watch body language at quiet moments, not just during meetings. A cat that stops using parts of the home, hides for long stretches, or eats only at night is telling you the arrangement is not yet working, even if there has never been a chase. Adjust space and supervision before small stress becomes a behaviour problem.
When the pairing needs extra caution
A nervous, elderly, or very small cat, or a Beagle with a known history of catching wildlife, raises the stakes enough that professional guidance before adoption is wise. Kittens need particular protection from an adult hound's clumsy enthusiasm, and introductions there should stay at barrier stage longer. Never leave a newly introduced pair alone together until weeks of boring, supervised coexistence have passed.
Choosing a Beagle already proven with cats smooths everything, and KinsLe Transferrable Profiles make that proof visible by carrying the dog's cat history and introduction notes from the previous home into yours.