Without a primary key, it's not possible to uniquely identify a row, so you will not be able to update specific records.
The best thing to do is to cease all imports to this data extension, export it and re-import it to a new data extension that has identical fields but at least one primary key that you wish to use to uniquely identify rows in the data extension. You will then easily be able to update this dataset in Marketing Cloud.
An alternative route (if using bulk upload method via SFTP) would be to change your import configuration to 'overwrite'. This would mean sending the entire dataset for each import however.