The board of trustees of the Starfleet Academy was a group within Starfleet Academy involved with prescribing the requirements for and the awarding of degrees to students. The board was headed by a president.
As such, they were mentioned prominently on Patricia F. O'Malley's diploma when she received the degree of Master of Astronautics upon their recommendation in 2153. The signature of the board president, Herman Zimmerman, was on the diploma. (ENT: "Storm Front, Part II")
The "Trustees of Starfleet Academy" were also mentioned in Star Trek Generations in an unseen portion of the Picard family album as the issuers of an invitation to the graduation of the class of 2327 at Yuri Gagarin Hall.
Furthermore, this may be the same group as the Starfleet Academy Board mentioned in Star Trek.