Title: Official
Content:  An official is someone who holds an office (function or mandate, regardless whether it carries an actual working space with it) in an organization or government and participates in the exercise of authority, (either their own or that of their superior and/or employer, public or legally private). An elected official is a person who is an official by virtue of an election. Officials may also be appointed ex officio (by virtue of another office, often in a specified capacity, such as presiding, advisory, secretary). Some official positions may be inherited. A person who currently holds an office is referred to as an incumbent. Something "official" refers to something endowed with governmental or 
Title: Authority
Content:  In the fields of sociology and political science, authority is the legitimate power of a person or group over other people. In a civil state, authority is practiced in ways such a judicial branch or an executive branch of government. In the exercise of governance, the terms authority and power are inaccurate synonyms. The term authority identifies the political legitimacy, which grants and justifies the ruler’s right to exercise the power of government; and the term power identifies the ability to accomplish an authorized goal, either by compliance or by obedience; hence, authority is the power to make decisions and the legitimacy to make such legal decisions and order their execution.
Title: Official
Content:  The term officer is close to being a synonym (but has more military connotations). A functionary is someone who carries out a particular role within an organization; this again is quite a close synonym for official, as a noun, but with connotations closer to bureaucrat. Any such person acts in their official capacity, in carrying out the duties of their office; they are also said to officiate, for example in a ceremony. A public official is an official of central or local government.
Title: Plenary power
Content:  A plenary power or plenary authority is a complete and absolute power to take action on a particular issue,  with no limitations. It is derived from the Latin term plenus ("full").
Title: Minister (Austria)
Content:  she is vested with management authority (Leitungsgewalt), meaning the minister is in charge of setting policy, of most personnel decisions, and of the internal governance and discipline of their respective departments. He or she also has injunction authority (Weisungsgewalt), the power to issue orders (Weisungen) to the civil servants in their respective departments that require or prohibit specific substantive acts and decisions. Both powers follow from the postulate that supreme executive organs hold ultimate responsibility; an organ cannot be considered responsible for what it cannot effectively control. There are departures from this general principle, however. Some subdivisions of ministerial bureaucracies can be declared "independent" ("weisungsfrei") by law; an "independent" subdivision is subject to management authority but not injunction authority.
Title: Officer of the United States
Content:  of the "sovereign power of the United States". Delegation of "sovereign power" means possession of the authority to commit the federal government of the United States to some legal obligation, such as by signing a contract, executing a treaty, interpreting a law, or issuing military orders. A federal judge, for instance, has been delegated part of the "sovereign power" of the United States to exercise; while a letter carrier for the United States Postal Service has not. Some very prominent title-holders, including the White House Chief of Staff, the White House Press Secretary and most other high-profile presidential staff assistants, are only employees of the United States as they have no authority to exercise the sovereign power of the federal government.
Title: The powers that be
Content:  In idiomatic English, "the powers that be" (sometimes initialized as TPTB) is a phrase used to refer to those individuals or groups who collectively hold authority over a particular domain. Within this phrase, the word be is an archaic variant of are rather than a subjunctive be. The use of are in this phrase ("the powers that are") is less common. "The powers that were" (TPTW) can also be found.
Title: Supreme executive organ
Content:  vested with management authority (Leitungsgewalt), meaning they are in charge of setting policy, of most personnel decisions, and of the internal governance and discipline of their respective bureaucracies in general. They also have injunction authority (Weisungsgewalt), the power to issue orders (Weisungen) to their respective subordinate organs that require or prohibit specific substantive acts and decisions. Both powers follow from the postulate that supreme executive organs hold ultimate responsibility; an organ cannot be considered responsible for what it cannot effectively control. There are departures from this general principle, however. Some subordinate organs are "independent" ("weisungsfrei"); they are subject to management authority but not injunction authority.
Title: Law of agency
Content:  Express actual authority means an agent has been expressly told they may act on behalf of a principal.
Title: Power behind the throne
Content:  The phrase "power behind the throne" refers to a person or group that informally exercises the real power of a high-ranking office, such as a head of state. In politics, it most commonly refers to a relative, aide, or nominal subordinate of a political leader (often called a "figurehead") who serves as de facto leader, setting policy through possessing great influence and/or skillful manipulation. The original concept of a power behind the throne was a Medieval-era figure of speech referring to the fact that the monarch's policies could be set by a counsellor not seated in the throne but standing behind it—perhaps whispering in the monarch's ear—out of common sight. In recent times, family members and official or unofficial advisers might take on a similar role. Sometimes it is difficult to assess whether such an accusation is true or a conspiracy theory.

Question: which term is used to identify having official power to act?
Answer: authority.
Authority.