can I get a new battery installed in my 2013 Macbook Air?

Welcome to Apple Support Communities.

Although your Mac is obsolete per Obtaining service for your Apple product after an expired warranty - Apple Support,

Apple does include this:

Service and parts may be obtained for longer, as required by law or for up to 7 years, subject to parts availability. Additionally, Mac notebooks 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.

Check with Apple Support to see if you qualify: Get Support.

Cheers,

Jack

under this extended service for battery only replacement (not offered by Apple Support "Communities" in English (Australia) I might assume my MBP 17inch early 2011 might still be eligible for a few more weeks, but the question is . . . . . is there anyplace here in JAPAN where this could be done since sending the machine (and existing battery, plugged in) might be accessible not by mail or "air" since that is now ± illegal (maybe except for Chinese) world wide?