Yes, you can either convert or move your existing Trading & DEMAT account to an NRO trading & DEMAT account or close your resident account and open a new NRI account. You are not allowed to convert an individual resident account to an NRI-NRE account. Documents required to convert your resident trading account to NRO account are as follows-
In case you want to update your account to the NRI (NRE) account, you need to close your existing resident account and open a new NRI (NRE) trading account. Share transfer between resident account and NRI (NRE) account is not possible.