Unfortunately, iFixit does not sell the battery for this tablet. :-(
However, you can buy a new battery for your tablet [https://www.ebay.com/p/Samsung-T4500E-T4500u-OEM-Tablet-Battery-for-Galaxy-Tab-3-10-1-Gt-p5210-P5200-US/2159865983|here].
Unfortunately, iFixit does not sell the battery for this tablet. :-(
However, you can buy a new battery for your tablet [https://www.ebay.com/p/Samsung-T4500E-T4500u-OEM-Tablet-Battery-for-Galaxy-Tab-3-10-1-Gt-p5210-P5200-US/2159865983|here].