The phrase "to know the staff" means to be familiar with and have a good understanding of the people who work in a particular organization or business. Full definition
Get to know the staff at your veterinary hospital; they will be a valuable resource for you. (texvetpets.org)
We make sure that clients know the staff members who are helping the lawyer on the case and encourage regular updates about the status of the cases. (idahopersonalinjuryattorney.com)
We didn't know the school as well as we would have liked, didn't know the staff, or even the name of our son's teacher. (educationnorthwest.org)