How to use subway pass on through services

Understand that there are multiple through services in Tokyo that is operated by Tokyo Metro and Toei such as the Tokyo Metro Fukutoshin that will continue to travel to Yokohama Station at Shibuya Station as Toyoku line.

How do I use the Tokyo Subway pass in this instance? Do I have to disembark at Shibuya (the last Tokyo Metro station) and purchase another new ticket to Yokohama or is it possible for me to stay in the train and travel all the way to Yokohama Station with the Tokyo Metro pass and pay for the difference when I arrived?

Thanks

Do you mean the Tokyo Subway Ticket? http://www.tokyometro.jp/en/ticket/value/travel/#anc03

It is valid on both Tokyo Metro and Toei, so there is probably no need to disembark.

I think the OP means when take subway Tokyo Metro Fukutoshin line to Shibuya and the train goes through to Tokyu Toyoko line to Yokohama, getting off at Shibuya is a must or not. I am not familiar with these lines, but searching on the net I found some Q&A about this situation. The answer says that you don't need to get off, but when you reach Yokohama, you need to pay at a manned booth, showing your day pass.

Not so hard :)

No need ticket gate out of pass border station
just doing "fare adjustment" at get off station at manned gate with paying in cash.
or use fare adjustment machine[のりこし精算機 norikoshi seisan-ki] near ticket gate like this.
https://youtu.be/XO13OrubR2A
(outed new 30Y/円 adjustment ticket for automatic gate insert/no need manned gate)
Fare adjustment machine paying possible by Suica/PASMO or(as IC card)'s SF(stored fare/charge).

If can't find adjustment machine in short time just say with showing pass
"Norikoshi seisan onegai-shimasu[乗越(のりこし)精算 お願いします。]" in JP.
Maybe gate staff understanding "Fare adjustment pls!" in EN.
or "Need fare adjustment? How much?" or simple EN maybe possible.

Usually through services do no require to buy separate tickets, depending of the situation you should be able to pay full fare at the begining or (as you have told) with the fare adjustment machines you finish your trip. And that's even easier when you pay with IC cards (SUICA, PASMO etc).