Macbook Pro late 2013 battery replacement

Apple is not usually here. These are end user forums.

Use this Apple support page to see if the computer is supported for battery service, and to get a cost estimate:

Mac Repair & Service - Apple Support

It appears the oldest Macbook Pros that they service are 2015 models, but you can try.

Otherwise you a left with finding a provider that will deal with the hazards of removing the original glued-in battery. The cost from an independent service provider could be more than the computer is worth today.

If it's available, they're not listing it. But just because it's not listed doesn't mean that you can't get the service. You would just need to ask to find out. I got a battery replacement for my mid-2012 Unibody MBP last year back when they listed prices directly but didn't have a listing for my model. And the price was what was previously known for my model ($129 US).

Apple says that they might have battery replacements available for models up to 10 years after they've discontinued them. In your case it would be a complete top case replacement at a battery price. But it also comes with a lot of caveats since their intent is that a battery replacement service requires an exchange of a top case and keyboard in good enough condition that they can recondition it to provide another top case replacement. If you've got noticeable dents or deep scratches, or the keyboard doesn't work, then it might turn into a top case replacement service (at a higher price since they probably won't be able to salvage the part) and I'm not sure they would even do that since it's no longer considered a battery service.

Obtaining service for your Apple product after an expired warranty - Apple Support

Service and parts may be obtained for longer, as required by law or for up to 7 years, subject to parts availability. Additionally, Mac laptops may be eligible for an extended battery-only repair period for up to 10 years from when the product was last distributed for sale, subject to parts availability.