Cats are territorial by nature, and rushing an introduction is the most common reason a new cat and an existing one never quite get along.
Start with full separation and scent swapping — a blanket or towel traded between spaces lets both cats get used to each other before they ever meet face to face. Move to supervised visual contact through a cracked door or baby gate before allowing the same room. Keep early sessions short and calm, and don’t force interaction if either cat is showing stress signals like flattened ears or a puffed tail.
A good introduction can take anywhere from a week to a couple of months. Slower is genuinely better here.