how to add songs to old playlist

Which iPod shuffle model do you have? I ask because the 1st/2nd gen shuffle works differently, for loading songs, compared to 3rd/4th gen. This document shows the four types (4th gen is the current model).

Identify your iPod model - Apple Support

Also, how did you load the current songs on the shuffle? If the shuffle is 3rd or 4th gen, and you used the Manually manage music setting (not automatic syncing), you may be able to manually add new songs to what is already on the shuffle. If the shuffle is 1st or 2nd gen, or you used automatic syncing (with 3rd/4th gen), the shuffle is erased when you sync it with a new (different) iTunes library.

In any case, it's risky to only have songs stored on an iPod. The iPod can break, or become lost, or have data corruption (and require a Restore). So, you may want to offload the iPod's songs and add them to your current iTunes library, even if you can add new songs to the iPod. iTunes syncing is generally in one directly only, from iTunes library to iPod. You cannot use iTunes to transfer song files from iPod to computer (except for songs purchased from the iTunes Store). However, there are third-party methods and utilities that can transfer from iPod to computer. If you do an Internet search on something like "ipod music transfer," you should get some links (including an article by CNET on the topic).

Once the song files are on your Mac's drive, add them to your current iTunes library. After confirming all of your songs are there, you can sync your iPod shuffle as desired.

NOTE: Songs purchased from the iTunes Store can be downloaded again at no cost, from the iTunes Store Purchased screen

Download your past purchases - Apple Support