I purchased TurboTax software to do 2021 taxes.However cannot open on laptop since it is not an approved Mircrosoft app. Are there other options in order to use software?

It sounds like you are using Windows in S mode. You cannot run TurboTax in S mode. You have to either switch out of S mode or use a different computer.

Note that switching out of S mode is permanent. Once you switch out, you cannot go back to S mode.

Usually you get a choice with the Microsoft warning to install anyway.  Microsoft has placed this warning on most, if not all, software programs it itself does not sell or have created.  Simply click install anyway and you should be good to go.  Just keep you install key you received with the software handy as you will be asked for it.

@pvbound