You probably need to set up automatic syncing. And if your "old library" is on an older version of iTunes, you may need to update it to use a "new iPod." You can get it here
Connect the iPod and select it in iTunes. If the iTunes sidebar (along left side of window) is not showing, from the iTunes menu bar, under View, select Show Sidebar. The iPod should appear in the sidebar, under DEVICES. Click on it to select it.
With the iPod selected in iTunes, there is a row of buttons toward the top, starting with Summary. Click on Music next to Summary. This the iPod's Music screen, where you tell iTunes how to sync songs to the iPod.
Check the box for Sync Music. If your iTunes music library is small and fits completely on the iPod, you can choose to sync Entire music library. Then click Apply. With this setting, everything in the iTunes music library syncs to the iPod. Whenever you make a change to the iTunes library, such as adding new songs, iTunes automatically updates the iPod with the same changes, the next time it is connected (or when you click the Sync button). If this works for you, you don't have to read the rest.
Otherwise, you can choose to sync Selected playlists, artists, albums, and genres. A convenient way to use this setting is to create a new playlist in your iTunes library. You can call it "iPod Songs," or whatever you want. From your iTunes music library, add songs you want on the iPod, such as those iTunes Store purchases, to that playlist. Back on the iPod's Music screen, find "iPod Songs" under Playlists, and select (checkmark) it. When you click Apply, the songs from your selection sync to the iPod. Going forward, when you want to update the songs on the iPod, just update that playlist in your iTunes library (add/remove songs). The iPod does not need to be connected. The next time you connect the iPod (or when you click the Sync button), iTunes automatically syncs the same changes to the iPod.