An application for new ATM card is a formal letter written to the bank manager when you need a new ATM/debit card for your account. This is required when the card is lost, damaged, expired, or when you open a new account.
Below are simple sample formats you can edit and submit at the branch.

Sample 1: Request for New ATM Card
To,
The Branch Manager
[Bank Name]
[Branch Address]
Date: [Write Date]
Subject: Application for new ATM card
Respected Sir/Madam,
I hold a savings account number [Account Number] in your branch. Kindly issue me a new ATM card for this account so that I can withdraw cash and make transactions.
Account Number: [Number]
Account Holder Name: [Your Name]
Mobile Number: [Number]
I shall be thankful to you.
Yours faithfully,
[Your Name]
Signature
Sample 2: ATM Card Lost / Replacement
To,
The Manager
[Bank Name & Branch]
Date: [Write Date]
Subject: Request for new ATM card (replacement)
Respected Sir/Madam,
My ATM card linked to account number [Account Number] has been lost/damaged. Kindly block the old card and issue a new ATM card.
Thanking you,
Yours faithfully,
[Your Name]
Signature
Sample 3: Simple New ATM Card Request
To,
The Branch Manager
[Bank Name]
Date: [Write Date]
Subject: Application for issue of new ATM card
Respected Sir/Madam,
Please issue a new ATM card for my account number [Account Number] in the name of [Your Name].
Yours faithfully,
[Your Name]
Mobile: [Number]
Signature
These samples for an application for new ATM card can be submitted at the bank branch along with ID proof if required.