What kind of phones do you use?
If you want to transfer contacts from your old iPhone to the new iPhone, you can simply use iTunes.
1. Start iTunes, go to "Edit > Preferences > Devices", and check "Prevent iPods, iPhones and iPads from syncing automatically".
2. Plug old iPhone into computer via the USB cable. Click "File > Device > Backup iPhone", and then iTunes will start to make a backup for your iPhone automatically.
3. Connect new iPhone to computer with the USB cable, and choose "File > Device > Restore from Backup". Then pick up the backup of your old iPhone, and click "Restore".
4. iTunes will make a confirmation again, and you need to click "Restore" in the dialog. Then iTunes will start to restore your new iPhone like iPhone 7 with the backup of old iPhone.
Besides, here's also a guide to help you transfer contacts between iPhone and android phone.