Hi -I lived in DC for a majority of the year in 2023 but transferred to a new department at the same company then moved to TN in September. Where do i file?

If you lived in DC for much of the year, you should file a part-year resident DC return. Complete that return after you enter all of your income and deductions on the Federal return, and they will transfer over to DC. Enter the date you left that area.

Tennessee has no state income tax on salaries, wages, bonuses or any other type of work income. 

Although the state used to tax income earned from interest and dividends, it has repealed this starting with the 2021 tax year. It does, however, tax businesses on their gross receipts, and has sales and use taxes. See here for more information.