[Galaxy Tab 3 7.0 Android Development] ketut.kumajaya:
Try attached flashable zip. This package will root/re-root your device. Please check the updater script inside:

ui_print("*************************************");
ui_print(" Galaxy Tab 3 7.0 - Universal Root ");
ui_print(" ketut.kumajaya @ xda-developers.com ");
ui_print("*************************************");
assert(getprop("ro.product.model") == "SM-T210" ||
getprop("ro.product.model") == "SM-T211" ||
getprop("ro.product.model") == "SM-T215");
show_progress(1.000000, 0);
mount("ext4", "EMMC", "/dev/block/mmcblk0p14", "/system");
mount("ext4", "EMMC", "/dev/block/mmcblk0p17", "/data");
set_progress(0.200000);
ui_print("- Mounting filesystem");
ui_print("- Remove existing root");
package_extract_file("system/xbin/busybox", "/tmp/busybox");
set_perm(0, 0, 0755, "/tmp/busybox");
package_extract_file("cleaner", "/tmp/cleaner");
set_perm(0, 0, 0755, "/tmp/cleaner");
run_program("/tmp/cleaner");
set_progress(0.300000);
ui_print("- Extracting files");
package_extract_dir("system", "/system");
set_progress(0.500000);
symlink("busybox", "/system/xbin/[", "/system/xbin/[[",
"/system/xbin/adjtimex", "/system/xbin/arp", "/system/xbin/ash",
"/system/xbin/awk", "/system/xbin/base64", "/system/xbin/basename",
"/system/xbin/bbconfig", "/system/xbin/blkid", "/system/xbin/blockdev",
"/system/xbin/brctl", "/system/xbin/bunzip2", "/system/xbin/bzcat",
"/system/xbin/bzip2", "/system/xbin/cal", "/system/xbin/cat",
"/system/xbin/catv", "/system/xbin/chattr", "/system/xbin/chgrp",
"/system/xbin/chmod", "/system/xbin/chown", "/system/xbin/chroot",
"/system/xbin/clear", "/system/xbin/cmp", "/system/xbin/comm",
"/system/xbin/cp", "/system/xbin/cpio", "/system/xbin/crond",
"/system/xbin/crontab", "/system/xbin/cut", "/system/xbin/date",
"/system/xbin/dc", "/system/xbin/dd", "/system/xbin/depmod",
"/system/xbin/devmem", "/system/xbin/df", "/system/xbin/diff",
"/system/xbin/dirname", "/system/xbin/dmesg", "/system/xbin/dnsd",
"/system/xbin/dos2unix", "/system/xbin/du", "/system/xbin/echo",
"/system/xbin/ed", "/system/xbin/egrep", "/system/xbin/env",
"/system/xbin/expand", "/system/xbin/expr", "/system/xbin/false",
"/system/xbin/fdisk", "/system/xbin/fgrep", "/system/xbin/find",
"/system/xbin/flash_lock", "/system/xbin/flash_unlock",
"/system/xbin/flashcp", "/system/xbin/flock", "/system/xbin/fold",
"/system/xbin/free", "/system/xbin/freeramdisk", "/system/xbin/fsync",
"/system/xbin/ftpget", "/system/xbin/ftpput", "/system/xbin/fuser",
"/system/xbin/getopt", "/system/xbin/grep", "/system/xbin/groups",
"/system/xbin/gunzip", "/system/xbin/gzip", "/system/xbin/halt",
"/system/xbin/head", "/system/xbin/hexdump", "/system/xbin/id",
"/system/xbin/ifconfig", "/system/xbin/inetd", "/system/xbin/insmod",
"/system/xbin/install", "/system/xbin/iostat", "/system/xbin/ip",
"/system/xbin/kill", "/system/xbin/killall", "/system/xbin/killall5",
"/system/xbin/length", "/system/xbin/less", "/system/xbin/ln",
"/system/xbin/losetup", "/system/xbin/ls", "/system/xbin/lsattr",
"/system/xbin/lsmod", "/system/xbin/lsusb", "/system/xbin/lzcat",
"/system/xbin/lzma", "/system/xbin/lzop", "/system/xbin/lzopcat",
"/system/xbin/man", "/system/xbin/md5sum", "/system/xbin/mesg",
"/system/xbin/mkdir", "/system/xbin/mke2fs", "/system/xbin/mkfifo",
"/system/xbin/mkfs.ext2", "/system/xbin/mkfs.vfat",
"/system/xbin/mknod", "/system/xbin/mkswap", "/system/xbin/mktemp",
"/system/xbin/modinfo", "/system/xbin/modprobe", "/system/xbin/more",
"/system/xbin/mount", "/system/xbin/mountpoint", "/system/xbin/mpstat",
"/system/xbin/mv", "/system/xbin/nanddump", "/system/xbin/nandwrite",
"/system/xbin/netstat", "/system/xbin/nice", "/system/xbin/nohup",
"/system/xbin/nslookup", "/system/xbin/ntpd", "/system/xbin/od",
"/system/xbin/patch", "/system/xbin/pgrep", "/system/xbin/pidof",
"/system/xbin/ping", "/system/xbin/pkill", "/system/xbin/pmap",
"/system/xbin/poweroff", "/system/xbin/printenv", "/system/xbin/printf",
"/system/xbin/ps", "/system/xbin/pstree", "/system/xbin/pwd",
"/system/xbin/pwdx", "/system/xbin/rdev", "/system/xbin/readlink",
"/system/xbin/realpath", "/system/xbin/renice", "/system/xbin/reset",
"/system/xbin/resize", "/system/xbin/rev", "/system/xbin/rm",
"/system/xbin/rmdir", "/system/xbin/rmmod", "/system/xbin/route",
"/system/xbin/run-parts", "/system/xbin/rx", "/system/xbin/sed",
"/system/xbin/seq", "/system/xbin/setconsole", "/system/xbin/setserial",
"/system/xbin/setsid", "/system/xbin/sh", "/system/xbin/sha1sum",
"/system/xbin/sha256sum", "/system/xbin/sha512sum",
"/system/xbin/sleep", "/system/xbin/sort", "/system/xbin/split",
"/system/xbin/stat", "/system/xbin/strings", "/system/xbin/stty",
"/system/xbin/sum", "/system/xbin/swapoff", "/system/xbin/swapon",
"/system/xbin/sync", "/system/xbin/sysctl", "/system/xbin/tac",
"/system/xbin/tail", "/system/xbin/tar", "/system/xbin/taskset",
"/system/xbin/tee", "/system/xbin/telnet", "/system/xbin/telnetd",
"/system/xbin/test", "/system/xbin/tftp", "/system/xbin/tftpd",
"/system/xbin/time", "/system/xbin/timeout", "/system/xbin/top",
"/system/xbin/touch", "/system/xbin/tr", "/system/xbin/traceroute",
"/system/xbin/true", "/system/xbin/ttysize", "/system/xbin/tune2fs",
"/system/xbin/umount", "/system/xbin/uname", "/system/xbin/uncompress",
"/system/xbin/unexpand", "/system/xbin/uniq", "/system/xbin/unix2dos",
"/system/xbin/unlzma", "/system/xbin/unlzop", "/system/xbin/unxz",
"/system/xbin/unzip", "/system/xbin/uptime", "/system/xbin/usleep",
"/system/xbin/uudecode", "/system/xbin/uuencode", "/system/xbin/vi",
"/system/xbin/watch", "/system/xbin/wc", "/system/xbin/wget",
"/system/xbin/which", "/system/xbin/whoami", "/system/xbin/xargs",
"/system/xbin/xz", "/system/xbin/xzcat", "/system/xbin/yes",
"/system/xbin/zcat");
set_progress(0.700000);
ui_print("- Backup OTA recovery");
package_extract_file("backup-recovery", "/tmp/backup-recovery");
set_perm(0, 0, 0755, "/tmp/backup-recovery");
run_program("/tmp/backup-recovery");
set_progress(0.800000);
set_perm(0, 0, 0644, "/system/app/Superuser.apk");
set_perm_recursive(0, 2000, 0755, 0755, "/system/xbin");
set_perm(0, 0, 06755, "/system/xbin/su");
set_progress(0.900000);
set_progress(1.000000);
ui_print("- Done!");
unmount("/system");
unmount("/data");

Partition information from T210XXAMET recovery (system: /dev/block/mmcblk0p14, data:/dev/block/mmcblk0p17). Latest SuperSU.apk, su binary, and my self compiled busybox included. This package untested, flash it at your own risk!