So, I just received the iOS 15 update on my iPhone 6s but the download and install option isn’t clickable. What can be done please?

It tells you what you need to do. Connect to WiFi, not personal hotspot.

Read your screenshot.

You need a Wi-Fi network connection.

NOT a Hotspot!

You will also need a SIM to activate the phone after the update is downloaded.

Lawrence Finch wrote:

You will also need a SIM to activate the phone after the update is downloaded.

That is no longer a requirement. At least since iOS 12 if not earlier.

Then why do users report that they can’t activate, but can after they insert a SIM?

Lawrence Finch wrote:

Then why do users report that they can’t activate, but can after they insert a SIM?

There are many reason for activation to fail. I can assure you SIM is no longer required.