The phrase "to staff something" means to provide a group or organization with the necessary personnel to carry out its operations effectively. Full definition
Members of staff of Nigerian universities who have been on industrial action for three months called off the strike today. (nigeriapoliticsonline.com)
Claims are easy to sanctioned because of quick service of staff members of your company. (policybazaar.com)
The group had a chance to meet with staff at the hospital and could clearly see the improvements the care group had on the local community. (totalpolitics.com)