Exquisite control of the DnaA initiator is critical to ensure that bacteria initiate chromosome replication in a cell cycle-coordinated manner. In many bacteria, the DnaA-related and replisome-associated Hda/HdaA protein interacts with DnaA to trigger the Regulatory Inactivation of DnaA (RIDA) and prevent over-initiation events. In the Caulobacter crescentus Alphaproteobacterium, the RIDA process also targets DnaA for its rapid proteolysis by Lon. The impact of the RIDA process on adaptation of bacteria to changing environments remains unexplored. Here, we identify a novel and conserved DnaA-related protein, named HdaB, and show that homologs from three different Alphaproteobacteria can inhibit the RIDA process, leading to over-initiation and cell death when expressed in actively growing C. crescentus cells. We further show that HdaB interacts with HdaA in vivo, most likely titrating HdaA away from DnaA. Strikingly, we find that HdaB accumulates mainly during stationary phase and that it shortens the lag phase upon exit from stationary phase. Altogether, these findings suggest that expression of hdaB during stationary phase prepares cells to restart the replication of their chromosome as soon as conditions improve, a situation often met by free-living or facultative intracellular Alphaproteobacteria.