At the end of each season, any unspent Battle Token Tier Skips will be auto-spent on remaining rewards in a pre-set path along the Battle Map.
However, if Battle Token Tier Skips acquired through the Vault Edition put your bank over the max number of redeemable Battle Token Tier Skips in a season, those extra Vault Edition Battle Tokens that are not auto-spent will carry over to the next season.