In Episode IV: A New Hope, it is said:
Tarkin: You don't know how hard I found it, signing the order to terminate your life.
Leia: I'm surprised you had the courage to take the responsibility yourself.
Tarkin: Princess Leia, before your execution, I would like you to be my guest at a ceremony that will make this battle station operational.
Do we know how she was going to be terminated? Would they just shoot her, or were there other, more theatrical practices? She was a member of the Imperial Senate, after all, and a public figure.