The Appointments Clause states:
[The President] shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law: but the Congress may by Law vest the Appointment of such inferior Officers, as they think proper, in the President alone, in the Courts of Law, or in the Heads of Departments. [U.S. Const. art. II, § 2, cl. 2]
The Appointments Clause enumerates, or “provides,” four categories of specific positions: “ Ambassadors,  other public Ministers and  Consuls, [and]  Judges of the supreme Court.” But that list is not exclusive. The Appointments Clause also generally references “all other Officers of the United States.” This list of positions is subject to two limitations: “whose Appointments are not herein otherwise provided for, and which shall be established by Law.”
That phrase, “whose Appointments are not herein otherwise provided for,” is, admittedly, a mouthful. We think this phrase tells the reader that the appointment of “Officers of the United States” is limited to the processes announced in Article II, Section 2. This sub-clause directs the reader not to scour the remainder of the Constitution for other provisions that provide authority to fill other federal “Officers of the United States” positions—by election or by appointment. In other words, the Appointments Clause’s “not herein otherwise provided for”-language is not an invitation to search for other constitutional provisions providing authority to create or fill federal offices; rather, this language puts the reader on notice that no such constitutional provisions exist beyond the textual bounds of Article II, Section 2. We think any alternative reading that leads readers to look for other constitutional mechanisms to fill “Officers of the United States” positions is mistaken. The “Officers of the United States” are only those positions that are filled by Article II, Section 2 processes.