When your cat runs away in OSRS, you need to get a new one from Gertrude. I've been through this many times, and it's quite simple once you know what to do.
If your cat has disappeared, you'll need to visit Gertrude who lives west of Varrock. She will give you a new kitten for 100 coins. If you happen to have a Ring of Charos (a), you can select the color of your kitten.
This new kitten needs care to grow into an adult cat. If you're looking to buy OSRS gold to prepare for other pet costs, make sure you have enough for food as well.
Your kitten needs regular attention to grow into a cat:
- Feed it regularly with fish or milk
- Pet it when it meows
- Let it follow you for about three hours
After three hours of proper care, your kitten will grow into an adult cat. Adult cats won't run away like kittens do, so you won't need to repeat this process.
If you're busy mining and need to know how to fix ore cleaning in OSRS, you can do that while your kitten follows you.
Remember that cats provide benefits like catching rats and completing quests, so it's worth taking the time to get a new one and raise it properly.