👍 As long as your device is the same platform then yes, you can. Unfortunately it's not possible to transfer purchases made on an Android device to an iOS device or vice-versa.
If you're on iOS, please visit the game's Settings which are accessible from the Main Menu. There you will find a "Restore Earlier Purchase..." option. Tap that and enter the same credentials you used when you made your purchase on your old device. As long as you're using the same Apple ID, your purchase will be restored at no cost.
On Android, simply visit your device's general settings and make sure you are signed into the same Google Play Services account you used when you made your purchase on your old device. The next time you launch BitLife, your earlier purchase should restore automatically.