Q: Reinstalltion of macOS sierra

You need to supply more info than you have. Which MacBook Air? What have you tried? What happens when you try? etc.

Which MacBook Air, year or model identifier?

If you were stuck on the screen you posted it would seem there is a connection problem. I would restart and try again.

Click on install Mac OS X .

Click on continue , agree , then again click on agree .

Click on Mac HD  , it will take time to install .

Select your region & click on continue .

Check the box show all & click on keyboard - click on continue .

Select wi fi network & enter your password .

Don’t transfer any information now .

Click on continue .

Check the box enable location services on the Mac .

Don’t sign in Apple ID password and click on continue .

Enter verification code and click on agree .

Create a computer account check the boxes full name , a/c name , password - click continue .

Select the boxes turn on file vault , allow my I cloud a/c to unlock my disk .

All your files in i cloud - uncheck store files from documents & desktop , diagnostics & usage - uncheck the two options

Check the box Siri on my Mac .

Setting up my Mac - its done

the OP's problems is the install is stuck. Not how to install. You really need to start reading the posts more carefully.

Let the small rotating circle be completed that is loading installation information as it is showing that computers eligibility is verifying , then one can click on bottom side option continue .

According to his posts, it's been stuck on that screen for 3-4 hrs.