-ate (office of) +
(Latin: a suffix; office of, office holder)
cardinalate
The rank or office of a Roman Catholic cardinal.
consulate
The political office or period of office of a consul, or the jurisdiction of a consul.
delegate (DEL uh gayt")
1. Someone who is authorized or sent to speak and act for others; representative, as at a convention: "Every state will send a delegate to the convention."
2. To entrust (authority, power, etc.) to a person acting as one’s agent or representative; entrust, assign, give over, charge, commit to the care of: "She delegated her power of attorney to her nephew."
A delegate is a person sent with authority to represent another or others; to delegate work or authority is to transfer or send it to someone else.
diaconate
The position of deacon or deaconess, or the term of office of a deacon or deaconess.
directorate
The office or position of a director.
emirate
The rank or office of an emir.
episcopate
The office, position, or term of office of a bishop.
pontificate
To officiate as a bishop, especially when celebrating the Mass.
presbyterate
1. The office of a presbyter.
2. A body of presbyters.
professorate
The rank, office, or term of office of a professor.
secretariate
The officials or office entrusted with administrative duties, maintaining records, and overseeing or performing secretarial duties; especially, for an international organization; such as, the secretariat of the United Nations: "He was a United Nations secretariat."
vicariate
1. The authority or office of a vicar.
2. The district under a vicar's jurisdiction.