How often have you seen or heard this construction?
There’s three reasons to buy your tickets early.
Omit the contraction and you will see you are saying, There is three reasons to buy your tickets early. There is three?
To restore agreement to your sentence, you need to write, There are three reasons…. Making that into a contraction, however, is awkward: There’re three reasons…. Ick.
Starting sentences with There is or There are (or Here is or Here are) is a weak construction. Better to write, Buy your tickets early for three reasons—and then list them.