Download and install is grayed out

Do you have a MDM profile?

If so, contact your company - IT department.

If it is a private iPhone you can update your iPhone to iOS 16.5.1, check -> iPhone models compatible with iOS 12 -> iOS 16 -> iPhone models compatible with iOS 16 – Apple Support (UK)

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%.

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

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

To update over the air from the phone all of these requirements must be met:

• You need at least 10 GB of free storage for iOS 16 or 6 GB for iOS 15 or lower; more is better
• You must be connected to a Wi-Fi network (and not a personal hotspot) unless it is an iPhone that supports cellular 5G (12, 13, 14 or SE 3rd edition) and has a 5G network connection
• The phone must be charged to at least 50%, and preferably plugged in so it stays above 50% during the update
• The phone must not be in Low Power Mode
• The phone must not be connected through VPN, and it may be necessary to delete any VPN apps and VPN profiles
• The phone cannot be in Airplane mode and must have a cellular data connection
• You cannot still have a beta of a previous version installed on the phone
• You cannot have a previous version that was downloaded, but not installed - go to Settings/General/iPhone Storage to look; if you find an iOS installer, delete it

If you can't meet all of them you can still update using your computer.