Can an NRI convert no-PIS account to a PIS account?

Yes, whenever you want you can convert NRE or NRO non-PIS account to a PIS account.

To do so, you have to submit a PIS application form to the respective bank where you have an NRI bank account. The designated bank on your behalf will submit the application to RBI to obtain PIS certificate.

You have to pay applicable PIS account opening fee, PIS account maintenance charges, and contract charges on the PIS account. Once your account is converted to PIS account, the fund settlement will be done through PIS account and there is no need to transfer funds to/from your trading account.