Librarianship is the work and the profession of a librarian — the job of looking after a library, helping people find books and information, and running that place well. It is not a person. The person is a librarian; librarianship is the field, the skill, and the career. You study librarianship, go into librarianship, take a degree in librarianship. It is a formal work-and-training word; everyday English just says “working in a library” or “being a librarian.” The ending -ship here means “the state or job of being that person,” as in friendship or leadership, though those feel more ordinary. Built from librarian plus -ship. Though actually, people outside the job almost never say it; you will meet it on university pages and in serious talk about the profession, not in “Where does she work?”