How to transfer new music from itunes to my iphone?

I just got a new computer and it made me download the new version of itunes. I don't have a lot of purchased music on my iphone because of old CD's I used to have, etc. When I plug in my phone it threatens to delete my music and sync the songs that they have (like the 4 sample songs they give). I want to keep all the music on my phone while still adding new songs which I put into my itunes. Is there a way to do that without deleting all the music already on my phone?