Link obtains this symbol of service from the Postman, who can be found on the Third Day, distressed about wanting to flee. After Link shows him the Priority mail, he'll pull himself together and quickly deliver Kafei's Letter to Madame Aroma. The Postman will meet up with Link outside the Milk Bar and give him the Postman's Hat, telling him that he has decided to flee Clock Town. The Postman will run off happily, leaving Link to his important deliveries.
The wearer can use the authority that comes with the mask to check inside mailboxes. The first time Link does this he will find a Piece of Heart and nothing but green Rupees afterward.
Receiving the Postman's Hat
Link obtaining the Postman's Hat.
↑ "Ohhh...I want to flee! B-but, it's not written on the schedule. T-to me, the delivery schedule... It's the h-highest priority." — Postman (Majora's Mask)
↑ "I have decided to flee. It is an order from the Postmaster. I am now free! I can set my own schedule!" — Postman (Majora's Mask)
↑ "You are doing a great job. Ka-ching! Some item other than a letter has been deposited. Ka-ching! Nice work. Ka-ching!" — Postbox (Majora's Mask)