The answer to your question is that you will enter your Schedule K-1 (from Tennessee) in the federal side of the TurboTax program, just as you would with any other K-1. To do this you can locate the Find / Search box in TurboTax, type in the exact search term "k-1" and click the button. Then you can click on the Jump To link that will appear directly beneath in the search results. This will take you to the main interview screen where you can input your Schedule K-1 data. Please see the screen-capture image directly beneath this text for a visual illustration; simply click the picture to open.
As a full-year Georgia resident, you are taxed on all of your income, earned everywhere (including from an out-of-state source, such as a Schedule K-1 from Tennessee). Thus, this one entry in the federal portion of the program will completely take care of your issue. What this means in practical terms is that your Schedule K-1 income will be taxed on both your federal and Georgia returns.Fortunately, Tennessee imposes no tax (on you) for this type of income. Thus, you won't have any special entry to make for Tennessee, or face an issue of "double taxed" or "mutually taxed" income, as you would if you this Schedule K-1 were instead for an activity conducted in a state that has its own income tax, such as South Carolina. In such an instance, you would have two states taxing the same income (Georgia and South Carolina), which would then further involve claiming a tax credit on your Georgia return for taxes paid to South Carolina on that same income.
However, the matter is very much simplified in this instance -- where we are discussing Georgia and Tennessee -- since only one of these states (Georgia) imposes an income tax. Therefore, after you enter your Schedule K-1 into the federal side of TurboTax, and indicate to the program that you are a full-year Georgia resident, this will resolve things . . . and result in you (correctly) being taxed by the federal IRS and by the state of Georgia, on your Schedule K-1 income, but not by the state of Tennessee.
(Note that if the entity that generated the Tennessee Schedule K-1 for you in the first instance conducts business activities in Tennessee, then it may face a sales tax burden itself, as although Tennessee has no income tax, it does rely on, and impose, a state sales tax on businesses.)
Thank you for asking this important question.