The contacts are either in the old phone's storage or at
Google Contacts . If they're not at Google Contacts, see the
contacts section of
Backing up an Android Device. Export from the old phone, then import to the new phone.
(The only reason to keep numbers on the SIM card was back when that was the only storage on a phone. Since smartphones, there's no reason for it, and Google has finally removed the capability. Even if you want the contacts from another account, just add the account to the phone and it will sync them. Then remove the account when you're done and it will eventually delete the added contacts.)