Hello DarrylS2,
Ensuring you're able to enjoy all your music on your iPhone is important. If the songs on your iPhone are not in iTunes on your PC, syncing the new music would cause those songs to be removed. There are a couple of solutions available. If these songs were purchases made in the iTunes Store, those songs would remain accessible on your iPhone. You can also download those songs in iTunes on your PC, then sync those songs back to your device as outlined in the steps below and following article.
- "Open iTunes and connect your device to your computer with a USB cable.
- Click the device icon in the upper-left corner of the iTunes window. Learn what to do if you don't see the icon.
- From the list under Settings on the left side of the iTunes window, click the type of content that you want to sync or remove.* To turn syncing on for a content type, select the checkbox next to Sync.
- Select the checkbox next to each item that you want to sync.
- Click the Apply button in the lower-right corner of the window. If syncing doesn't start automatically, click the Sync button."
Use iTunes to sync your iPhone, iPad, or iPod with your computer
If these songs were synced to the iPhone from another computer and originated from a third-party source such as a CD, you would have to add those CD's to iTunes on your computer before syncing. This would ensure the songs remain on your device. The next option that's available would be to subscribe to Apple Music. This would allow your songs to sync between your devices. You can learn more about Apple Music via the following article.
Music - Official Apple Support
Take care!