When you need to surrender plate(s) 
Before you end the vehicle's liability insurance coverage. If you do not turn in your plate , we will suspend your registration and can suspend your driver license. If you want to register your vehicle in another state. You must surrender your New York State vehicle plates to the New York DMV. 

How to surrender New York State plates 
Note: If you need to surrender plates from another state , you need to surrender them to that state's DMV not the New York State DMV. 

By mail 
Step 1 : Remove plates and stickers This includes the plate frames and fasteners - we will not accept plates with them attached. Destroy the registration and inspection stickers from your windshield. Do not give your plates to another person unless that person will surrender the plates for you. Step 2 : Complete the PD-7 application You must complete the Plate Surrender Application PDF [1] PD-7 for each set of plates you are surrendering. Step 3 : Mail the application with your plates to NYS DMV6 Empire State PlazaRoom B240Albany, NY 12228 We use the mail postmark date as the date that you surrendered your plates. To be notified by the US Postal Service that we received your plates, send them by registered or certified mail, and request a return receipt. We will mail you your FS-6 T receipt. 

At a DMV Office 
Step 1 : Remove plates and stickers This includes the plate frames and fasteners - we will not accept plates with them attached. Destroy the registration and inspection stickers from your windshield. Do not give your plates to another person unless that person will surrender the plates for you. Step 2 : Complete the PD-7 application You must complete the Plate Surrender Application PDF [1] PD-7 for each set of plates you are surrendering. Step 3 : Bring the plates and PD-7 to an DMV Find a DMV office [2] near you. County motor vehicle offices will charge you a $1 fee to process the surrender. If another person surrenders your plates for you , make s

user: Morning! I need some information about surrendering plates. I'd like to know, when do I have to surrender them?

assistant: Morning, Mr. You have to surrender your plates before you end the vehicle's liability insurance coverage, or when you will not use the registration. 

user: I have a trailer, and my plate got stolen on a trip to the beach. I found out yesterday I had no plate, what should I do? 

assistant: Don't worry,  as you may already know: "normally" a trailer does not need liability insurance, so DMV will not suspend your driver license or registration because your plate got stolen, and therefore you will fail to surrender it.

user: So, just to make sure: do I need yo surrender trailer plates? 

assistant: You must surrender your plate if your trailer doesn't have a valid registration, it's ok if you "lost" it as long as your registration is valid. 

user: Ok, thanks for that! Btw, my girlfriend wants to surrender her plate, but she's very new with this stuff.. Could you send me some information on how to surrender plates by mail? So that I can send it to her, please,

assistant: Yes, sure!
First, you need to remove the plate and the stickers on it. Then go to www.dmvplatebymail.com and download de PD-7 application, and after that mail us the application to: NYS DMV6 Empire State PlazaRoom B240Albany , NY 12228. 
When we got all that, and after your application has been accepted we'll mail you your FS-6 T receipt.

user: Ok, one last question. You told me that's it's ok to have gotten my plate stolen for trailer, because the liability insurance is not a MUST, and as long as I have a valid registration I'll be fine. But what If I have a car, and the plate is lost, stolen, or destroyed?

assistant: In that case, you need to report the plate as "stolen, lost or destroyed" and immediately surrender the registration. DMV will issue you a new plate and registration. 

user: What if I'm in an another state? Would it be a problem? Or can I do the whole process by mail as if I was here?

assistant: You have to go to that state's DMV agency and surrender them there, but you can still surrender them by mail. Just make sure, you are in that specific state when you are in the DMV website.