Hi,
If you're using the Auto-Sync feature for your contacts to be transferred, it may not be able to copy all of the contacts stored from your old phone. This maybe because your contacts were saved locally or onto a SIM. In this case, you can try to export your contacts from your old phone to the new one using an SD Card.
Go to Contacts -> Settings button -> Import/Export -> Export to SD card
In this way, you can use the SD Card to import your contacts to your new phone. Let me know if this step worked for you. Thanks!