You can learn about becoming a Deputy Borrower at the Columbia University Libraries and find the online form your supervisor must submit here

All items borrowed on the Deputy Borrower account become the sole responsibility of the Faculty Member or Administrator.

Neither the Deputy nor the Supervisor may have any outstanding fines or library obligations at the time of application or renewal. 

Becoming a Deputy Borrower at the Gottesman Libraries at Teachers College is a separate process. See how here.