The short answer, yes!

Pentanet does not have the authority to close your account with another provider. You'll need to arrange this with your previous provider.

However... 

When changing providers on the nbn™ network it's best practice to wait until your connection has been transferred (churned) to Pentanet before you cancel with your existing provider. In some cases, a cancellation order lodged with nbn™ before a transfer has taken place may delay connection which could leave you without internet service!  

When you're live on the Pentanet network, we recommend giving your previous provider a buzz, just to let them know you’ve now left for billing purposes – we wouldn’t want them charging you for a service they aren’t providing! 😉