"To run the ship" means to be in charge or to be responsible for overseeing and managing a particular situation or organization. It implies being the person in control and making important decisions. Full definition
He feels like she is saying he is failing in his responsibility of running the ship by not supporting her in her tasks. (tribecaplaytherapy.com)
Was that just kind of running things really tightly, running the ship as tightly as possible, was it a discrepancy in the understanding of demand? (gonintendo.com)
We have a good squad of players, an average captain running the ship. (justarsenal.com)