how long is the appointment to install a new battery

I had it done same-day at an Apple Authorized Service Provider.

Made an appointment in advance, backed up and prepared the phone, dropped it off with them, came back a few hours later (the same day) and picked it up. No issues – other than that they peeled off my old screen protector.

Battery service

We can replace your iPhone battery for a fee. Our warranty doesn’t cover batteries that wear down from normal use.

Your product is eligible for a battery replacement at no additional cost if you have AppleCare+ and your product’s battery holds less than 80 per cent of its original capacity.

Find out more about iPhone battery service

For reference: Prepare your iPhone or iPad for service - Apple Support