Yes, it's the most obvious solution to run 'chmod 777 /drive -R' where /drive is a mount point of your external drive.
But it's not the optimal solution if you still need to manage permissions for the files and folders on this drive.
For example, you may need to access restrict for one user to some folder or set a read-only access to him.
If you plan to use some applications like Samba on this drive you'll also need it.
If you're interested you can pick more information about permissions here.