You can import old workouts to your new phone in all other cases except if your new phone is a Symbian phone. Sports Tracker for Symbian phone's doesn't support syncing the workouts both ways, ie. it only sends the workout to the web service.
When your new phone is something else you need to:
1) Connect to Sports-Tracker-service with your old phone if not yet connected and sync all your workouts to the web service.
2) Once the workouts are visible in www.sports-tracker.com in your profile, then just connect your new phone to the service with the same account details and your phone will automatically sync all your workouts.
Note: Deleting a workout from web will delete it from your phone and vice versa. So never delete a workout unless you're sure you don't need it anymore.
Contact Us inside the app
Android: Settings - Help
iOS: Profile - Help & Feedback