You'll then be able to go back and do some of these quests - but not all of them. If you have created a level 60 or 65 Outlander character, your main story objective will be to simply follow the Knights of the Fallen Empire expansion story.
This is not recommended for new players looking to enjoy the story. Starting a character at level 60 or 65 is referred to as using an Outlander Token, which starts you at the beginning of the later expansions. Most players start at level 1, but there is an option to create a level 60 or 65 character if you have subscribed recently or have bought the opportunity from the Cartel Market.
Special note for players who use an Outlander Character Token to create a Level 60 or 65 character:
The story quests in the game are meant to be played in a specific order, but in reality you may not come across them at the right time or might accidentally miss them all together while focusing on your main quest. If you are just beginning your adventure in Star Wars: The Old Republic, you may realize that there are an incredible number of quests available in the game, and a vast range of story and lore for you to explore.