Pls help, iTunes & iPhone account?

I had an old iTunes account that's now closed. I have music from the old account on my iPhone and had iTunes on my old broken laptop. I have tried to transfer the music from my iPhone to my new laptop but I cant but Im totally not bothered about this as its old crappy music anyway. So my question is, if I set up a new iTunes account and download music onto my new laptop, will I still be able to sync it with my iPhone and transfer the new music to it even though it has music from my other account on it? Im not fussed if the old stuff all disappears from my phone as its crap anyway. Hope this makes sense!! Thank you :-)