We will need the TypeScript Package to get Syntax highlighting to work. we will install the package using Package Control.
So, first go ahead and install Package Control
Now, go to preferences, where you can now find Package Control option, click on it .
from the drop down click on Package Control: install Package
and now search for typescript in the input area
click on TypeScript and wait for installation then restart Sublime text.
Now you should be able to see the syntax highlighting.
Here’s a simple video showing the above process!!