Currently NeSI users cannot authenticate with Globus using institutional credentials. Instead you need a Globus ID which becomes your username whenever you connect to Globus.
Go to https://www.globusid.org to create or set preferences associated with your Globus ID.
From https://www.globusid.org , select "Create A Globus ID".
Enter a username/password of your choice, and the value "NeSI" in the Organization field.
Your email address will be verified - check your email and copy/paste the verification code you receive into the next page and submit. Upon verification, your account will be enabled. Unless you have an pre-existing Globus account, press " Continue"
Your Globus registration is complete. Grant Globus permission to access your identity and act on your behalf by checking "Allow" on the next box.
You can now log into the Globus web app to transfer files.