Chaplaincy is either the job of being a chaplain, or the office, team, or little department where that work happens. A hospital may have a chaplaincy down the corridor; a university may advertise a chaplaincy that welcomes students of many religions, or of none. The -cy ending turns the person into the role or the place, the way presidency is the job of a president. In real talk, “she took a chaplaincy in the prison” means she took that post; “drop in at the chaplaincy” means go to the room. Both are normal.