Yes you can.
1. Select F3 to access the Split Tool. Then create an Event which defines the section of audio which you want to move.
2. To create an Event: Set the cursor over the beginning of the section you want to move and push/release the left mouse button. Go to the other end of the section you want to move and repeat push/release of left mouse button.
4. Select F1 for the Range Tool. Move the cursor over the new Event and hold down the left mouse button.
5. Move the Event anywhere you want and then release the mouse button. Done!
Watch this video to see this in action as well as learn how to “slip” an audio Event.
This guy does some great tutorials on Studio One. Here is the home page with a list. I recommend you watch all of them one at a time.