Is it necessary to have a customer complete a debit card application for a new card when they have already agreed to the terms and conditions of the account which includes the electronic fund transfers rights and responsibilities?

Documentation will be the key whether that is a written application or other record of the request:

§ 1005.5 Issuance of access devices.

(a) Solicited issuance. Except as provided in paragraph (b) of this section, a financial institution may issue an access device to a consumer only:

(1) In response to an oral or written request for the device; or

(2) As a renewal of, or in substitution for, an accepted access device whether issued by the institution or a successor.