I can't open a new tab on Safari on my iPad air

Try a reset: hold down the home button along with the power button until you see the Apple, then let go.

1. Settings>Safari>Clear History, Cookies and Data

2. Hold the Sleep/Wake and Home button down for about 10 seconds until you see the Apple Logo

Thankyou - worked for me and my new iPad Mini

I am glad it works for you 🙂