I want to download CBS All Access app to my AppleTV 4k but it wants me to start a free week trial

You would have to go into the app store on the Apple TV and download the app. What you are currently seeing is in the TV app, for the Apple TV channel version of CBS All Access, which is a separate subscription.

No problem. The TV app is a destination for keeping track of all (supported) subscription services. To keep the existing subscription you download the app and it will integrate with the TV app but kick out to CBS' app for playback. The Apple TV channel will play directly within the TV app, using Apple's servers, while also including family sharing and the ability to download content onto IOS and Mac devices.

If all viewing was done within the TV app, which the Roku and Firestick support, then it may be something to consider.

Certain people who recently purchased iPhones and other Apple devices can actually watch the new Apple TV Plus (aka Apple TV+) service for free for a year. This means having access to TV shows like For All Mankind, The Morning Show, and See right away without having to pay anything.  If you’re wondering how the “Free with an iPhone” special works with the new Apple TV Plus service, we have the details. Apple TV Plus offers new Apple Originals every month. The content is ad-free and on-demand as soon as each episode released. As an added plus, the service can be used by up to six family members, and episodes can be downloaded and watched offline. You might have heard that some people with iPhones and other Apple devices will get to watch Apple TV Plus for free rather than $4.99 a month. This is true, but with some limitations and restrictions.Only People Who Bought Eligible Devices After September 10, 2019 Qualify Only people who bought a new Apple device (such as an iPhone, iPad, iPod Touch, Mac, or an Apple TV) after September 10, 2019 are eligible for this offer. After the free trial, you will be charged $4.99 a month. In order to not be charged, cancel your subscription in the Settings menu any time after the renewal date. If you cancel before the renewal date, you’ll use your free one-year trial and you won’t be able to reactivate it. The device must have been purchased from Apple or an authorized reseller in order to get this offer. The offer is only good for three months after your eligible device was activated, starting November 1, 2019. In other words, you can’t redeem the free offer until November 1 or later. If you purchased your new device before November 1 (but after September 10), you will have three months to redeem the offering starting on November 1. After that, the offer must be claimed in the Apple TV app within three months after you first set up your new device.You Must Be Running the Lastest OS In order to be able to redeem the offer, your device must be running the latest iOS, iPadOS, tvOS, or macOS. So if you were eligible but couldn’t redeem the offer, try updating your device’s OS and see if that makes a difference. The offer can’t be combined with any other free trials or Apple TV Plus offers. And only one person per Family can use it, but the offer can be shared with five other family members through the Family Sharing feature. You can read the full terms and conditions here.How To Activate Your Offer To activate your offer, turn on your device and make sure you are signed in with your Apple ID. Open the Apple TV app on November 1 or later, making sure that your eligible device is running the latest OS. (The service will be available starting November 1 at midnight Pacific, which is 3 a.m. Eastern and 2 a.m. Central.) When you launch the app, the offer should immediately appear on your device. If it doesn’t, scroll down to “Watch Now” and the offer should appear on your screen. Tap on “Enjoy 1 Year Free.”