Can I transfer music from my iPod to iPhone?

There is no supported method of doing so. The media on the iPod had to be synced to it from the music library on your computer. The only other options are that the music was purchased from the iTunes Store, which means you can re-download it to your phone using the same Apple Account you used to purchase it to begin with, or you're using Apple Music, which means it's a non-issue and you can get it directly from Apple Music on your phone using your subscription.

Media sync from a computer is one way, computer to device. The media should still be in the music library on your computer. Sync it to the phone. If it's no longer in your media library, you will have to re-rip the original media (CDs) to the computer or re-download the media from the source you originally got it from or restore it from a backup.

If you no longer own the original media (i.e. CDs), then you no longer own the media and can't legally have it on your devices...

There are 3rd party products that claim to be able to extract the music from an iPod or iPhone to a computer, but their legality is questionable at best.