Assassination was an accepted and highly effective method of career advancement in the Terran Empire and Starfleet. Furthermore it was common practice for a first officer to receive orders to kill his captain if the latter failed to carry out a mission.
Examples include Jonathan Archer's assassination of Admiral Black and Archer's subsequent assassination by Hoshi Sato, as well as James T. Kirk's assassination of Captain Christopher Pike and Lieutenant Commander Spock being ordered to assassinate Captain Kirk in case the latter is not able to acquire any dilithium from the Halkans. (TOS: "Mirror, Mirror"; ENT: "In a Mirror, Darkly")