I want to download YouTube

The latest version of the YouTube app on iPhone now requires iOS 14 or later.

Please update. iPhone 6s supports up to iOS 15.x. Update your iPhone or iPad - Apple Support

iPhone 6s, iOS 13

If it is an iPhone 6S you can update to iOS 15.7.6, you can check by reading this Apple article:

iPhone models compatible with iOS 12 -> iOS 16.

iPhone models compatible with iOS 15.5 – Apple Support (UK)

Go to Settings -> General -> Software Update -> Download and Install.

You need about 6 GB device storage and good Service and/or Wi-Fi.

If they are On, turn Off Hotspot & VPN.

Charge the battery > 70%.

See the following Apple articles:

Update your iPhone, iPad, or iPod touch

Update your iPhone, iPad, or iPod touch - Apple Support (IN)

If your iPhone, iPad or iPod touch won’t update

If your iPhone, iPad, or iPod touch won't update - Apple Support

You can do the update via PC, see this Apple article: Update software on iPhone, iPad or iPod touch in iTunes on PC

Update software on iPhone, iPad or iPod touch in iTunes on PC – Apple Support (UK)

If you have a Mac see this Apple article: Update your iPhone, iPad, or iPod touch with the Finder

Update your iPhone, iPad, or iPod touch with the Finder - Apple Support

👉 After you have update your iPhone to iOS 15.7.6, you can ->  YouTube requires iOS 14 or later.