These maneuvers are advanced. Make sure you understand and do your research prior to attempting even a test transfer. I am not responsible for your crypto should you lose any. I am simply conveying the steps I took to move my own ERC20 tokens to my new hardware wallet.
Your Ledger Nano S is set up according to the manufacturer’s instructions (purchased ONLY from the ledger store or from amazon, never ebay where it could have been tampered with). Here’s a good video to help you through the process of setup, but you won’t install the chrome extensions, we’ll use MyEtherWallet (MEW) instead: https://www.youtube.com/watch?v=GPpZxOjvU10
Open MEW. Make SURE you are on the correct site so you don’t get phished! (You can’t access your Ledger on MEW with Firefox, use Chrome instead.) https://www.myetherwallet.com/
Add ICX to your custom tokens. https://medium.com/helloiconworld/how-to-add-icx-custom-token-df944450f998
Secure your ICX from the exchange onto your Nano S. You must enable your Nano S to work with MEW by logging into your Nano S, navigating to the Ethereum app, and setting the Browser Support to YES. ***If your hardware wallet is not recognized by your Linux computer, follow these instructions to correct that: https://ledger.zendesk.com/hc/en-us/articles/115005165269-What-if-Ledger-Wallet-is-not-recognized-on-Linux-
Binance charges 1 ICX for each transfer. I sent a test of a small amount of ICX first to make sure it went through to my Nano S before I sent the whole amount. You don’t need any ETH to send your ICS to your Ledger, but you will need some to send tokens from your Ledger.
Here’s a couple of video tutorials I watched and a ledger tutorial to secure my tokens on my Nano S:
https://www.youtube.com/watch?v=WzuPZrbNXeQ (he’s sending a different token and it’s from bittrex, but ICX from binance is similar except that I had the extra step of having to click a confirmation email)
https://www.youtube.com/watch?v=_RvDPQHERtc&t=301s (from boxmining’s youtube channel)
(This would also work for other ETH ERC20 tokens)