Do not make the mistake of doing it. It is possible that you'll continue to play your character Classic but you won't. This is particularly applicable if you've removed Naxxramas. It is possible to restart with a new character if you'd like to continue playing Vanilla. It's more enjoyable and fulfilling.

Individuals who wish to WOW TBC Classic Gold reach max but don't have the means to achieve it yet, can do it with changes to tbc or staying in classical. They can join new guilds, then start raiding nax completely starting from scratch by creating a new raid. They'll have to pay for a service that will create clones of them to begin the tbc. Since the original wow community has been dissolved The cloning process should be free.

Every server currently being used will be upgraded to TBC servers. New Vanilla versions of those servers will be available. You can choose to activating the character on either the Vanilla or TBC version. You will need to pay if you wish to activate the same character on both.

EDIT: From Blizz's own article on the topic. "On the day of patching, players will be able to open the Battle.net desktop app and choose the game you wish to play: Burning Crusade Classic, or WoW Classic. Both types of games will display your existing characters with the old realm name/s. After choosing a game, select a character you wish to buy WOW TBC Gold play and confirm. You can use an optional paid-for service to access the cloned character in the two game types if you want to play as your character on both. All you have to do is login as normal and start playing.