Week one belongs to scent, not meetings
Set your new cat up in a single room with her own litter tray, food, water, scratching post and at least two hiding places, and let your resident cat keep the run of the rest of the home. For the first days the cats should know each other only by smell and sound. Rub a soft cloth on each cat's cheeks and place it near the other's food bowl, swap their bedding, and feed both cats their tastiest meals on opposite sides of the closed door so the stranger's scent arrives paired with good things. Expect some hissing at the door from your resident — that is information gathering, not failure — and watch instead for eating, playing and sleeping returning to normal on both sides.
Let them see each other without touching
Once both cats eat calmly near the door and the cheek cloths get rubbed on rather than avoided, add sight in small doses. A door opened a crack and wedged, a baby gate, or a screen lets them look while a barrier does the keeping-apart for you. Keep these sessions short and built around food or play: toss treats, trail a wand toy on each side, and end while everyone is still relaxed, which might be two minutes at first. Hissing with ears up and a quick retreat is normal negotiation; fixed staring, flattened ears, growling that builds and attempts to lunge mean the session was too long, so step back half a stage without treating it as a disaster.
Open the door for short, supervised time
In the third week or so, if sight sessions are boring — and boring is the goal — let the new cat explore beyond her room while your resident is elsewhere, so she learns the house's smells and escape routes in peace. Then allow brief time in the same room, again arranged around a meal or a game, with a cushion or piece of cardboard ready to block sight lines calmly if tension spikes; never reach in with your hands between two aroused cats. A scatter of treats on the floor defuses most stand-offs, because heads go down and the spell breaks. Increase the shared time gradually, and keep the new cat's base room available with its door open so she always has somewhere that is hers to retreat to.
Resources prevent the quiet arguments
Most friction in a new two-cat home is not about dislike but about logistics. Provide litter trays in more than one place — the usual guideline of one per cat plus a spare, in separate spots, stops guarding before it starts — and duplicate the things cats argue over: food stations, water bowls, high perches and warm sleeping spots. Feed the cats apart at first, even after they seem friendly, because a bowl is the easiest thing in the world to defend. Play with each cat separately as well as together, so your resident's routine with you does not feel stolen, which matters more to acceptance than almost anything the new cat does.
What the end of the month should look like
True friendship — grooming each other, sleeping touching — may come in time, but it is not the bar for success. By the end of a well-run month, most pairs reach polite coexistence: moving around each other without drama, eating in the same home without guarding, and choosing their own spots. If you are still stuck at an earlier stage with genuine aggression rather than grumbling, slow down rather than forcing contact, and talk to the rescue, whose staff have managed hundreds of these introductions and can spot what your pair is telling you. KinsLe Messenger keeps the rescue's advice, your family's observations and any helper's notes in one conversation hub for the new cat, so the staged plan stays shared and nobody freelances a surprise face-to-face meeting.