A hearing aid comprises an input unit providing an electric input signal representing sound, a wake word detector configured identifying a particular wake word based on said electric input signal, and providing a wake word control signal indicative of whether, or with what probability, the wake word is detected, or an own voice detector estimating whether, or with what probability, the electric input signal originates from the voice of the user and providing an own voice control signal indicative thereof, transceiver circuitry establishing a communication link to another hearing aid allowing the transmission and/or reception of the electric input signal to/from the other hearing aid, and a pre-processor controlling the transceiver circuitry in dependence of the wake word control signal or the own voice control signal. A binaural hearing aid system and a method of operating a hearing aid are further disclosed.