Did you have your game connected to Facebook/Kingdom? If yes, then all your progress is stored there. All you'll have to do is to reconnect the game and you'll have your levels and highscores back.
If you still have the old phone then please boot it up, start Pet Rescue Saga and check if the game is connected. If not, then now is a good time to do it
If you don't have your old phone and it wasn't connected online then please get in contact with our support staff.