How to fix outdoor faucet drip when indoor shut off is off
Replace the indoor shutoff, as it's obviously not closing all the way. Alternatively, if it's a gate valve, you could try repairing it. Though in my opinion, you might as well replace it. Replacing it with a ball valve, is usually a good choice.

You'll also want to replace the outdoor tap, as it's also not working. Again, you could possibly repair it, but it's probably just as easy to replace it. If you live in an area with freezing temperatures, you'll want to replace it with a frost-proof sillcock.