Apart from the details requested by Ignacio, please let us know if you have a subscription for Lightroom mobile or if you were using the free version of the application earlier.
If you were using thr free version, the presets stay saved locally on the device and do not sync with the cloud storage. Hence, they would not be available on the new device you have purchased.
If you are using a subscription, please ensure that you are signed in to the application using the correct email. You can go to lightroom.adobe.com then select an image and go to the option to "Edit this Photo", to check if your presets have been synced with the cloud storage.