As said before, your iPhone only shows up contacts you have saved direclty from it, or synched from iCloud (if you have another Apple device where you saved them, connected to the same account). Given that the iPhone is new, there are a couple of ways to retrieve contacts from your old phone: if you had another iPhone before, and you actually can access it, you can just activate Contacts in the iCloud settings on both devices, and that should do the job, while, if you have no access to the device, you can restore or recover contacts only from a previous backup; if you are shifting from another phone, than there are different courses of actions, depending primarily on the the device type and software, and, importantly enough, if you used a SIM with it. If you have a SIM where all your contacts were stored, and you are using it on the iPhone, to see all of the contacts you have to manually import them, through Settings, as it's not an automatic process. Here's an article from Apple Support site that can shed light on the subject:
https://support.apple.com/en-us/HT202340
