Can I use Turbo Tax Premier or do I need to upgrade to Turbo Tax Business? I was added to a multi partner LLC on 12/31/23 and 2024 is the first yea receiving a K-1.

If you just receive a K-1 you can use any Desktop version.  If you use Online you will need the Premium version to enter a K-1.  You only need Turbo Tax Business to actually prepare the 1065 or 1120 tax return.  Don't confuse the Desktop Home & Business program with the stand alone Business program.  H&B is only for personal returns that need schedule C for self employment.