Your relationship sounds very unhealthy and unsustainable. You need to have contact with your friends- or at least the freedom to be able to. It’s really hard to have open conversations about this sort of thing with an insecure partner but in a perfect world you would sit down with your gf and tell her that you want to reconnect with your old best friend- that cutting her off was a hurtful thing to do and you want to make things right. You being friends with someone doesn’t mean you love your gf any less, but a healthy relationship requires honesty and trust.
Honestly if she is that insecure- she needs to fix that herself, it’s impossible for you to do that. All that being said I’m assuming your intentions are innocent and you’re not wanting to reconnect with your old bestie in a romantic way.