No, Final Draft 9 is too old to run on Big Sur or on a computer with Silicon (M) architecture. FD8 / 7 / 6 etc. are also too old.
Final Draft 13 runs without issues on these computers.
For information on upgrading to Final Draft 13, click HERE.
NOTE: Activation service for Final Draft 9 has been discontinued and this version of Final Draft is no longer activatable (or re-activatable) to run in full mode on any computer. The program will continue to work but only on a computer that is already activated and only if nothing is done to the computer that will deactivate it (such as an OS upgrade or a replacement hard drive).
Technical support (phone, chat and email) for Final Draft 9 and older is no longer available.