Start with a separate room for the newcomer, stocked with food, water, a litter tray, resting places and hiding spots. Give each cat time to settle before asking them to share space. Scent swapping with bedding can help them learn about one another without a face-to-face meeting.
Let comfort set the pace
Progress from scent, to brief positive experiences on opposite sides of a closed door, and only then to short visual meetings with a safe barrier. Keep sessions calm and give each cat an easy way to move away. Do not punish hissing or hiding; those are signs that the pace may need to slow.
Provide separate resources so neither cat has to guard food, water, litter or a favorite resting place. If one cat stops eating, avoids key areas or the tension continues, ask your veterinarian for help.