We propose a new form for the quantum master equation in the theory of open quantum systems. This new formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper times. In the Born-Markov approximation, we consider a quantum massless scalar field coupled with two-level systems. Starting from a separable state we show the emergence of entanglement harvesting. For different proper accelerations we verify also the entanglement sudden death.