Does the President approve a pardon granted by the US Supreme Court?

Answer 1

No, the system doesn't work like that.

The Supreme Court is not a trier of fact: they don't determine a defendant's guilt or innocence. When the Court agrees to review a case, it analyzes whether the legal procedures in a case were conducted in accordance with constitutional protections, and whether laws applied to a case were constitutional, but don't review material evidence or errors.

If the Court determines the appellant's constitutional rights have been violated and the case needs further attention, or the appellant deserves a new trial, they remand (send the case back) to the lower courts for disposition.

The Constitution does not give the Supreme Court the authority to issue pardons. Article II, Section 2 of the US Constitution confers this power on the President: "The President ... shall have power to grant reprieves and pardons for offenses against the United States, except in cases of impeachment."

This authority does not extend to people convicted under State laws, who would need to petition the Governor of that State for clemency.

Answer 2

No, the president does not need approval. Look at the constitution article 2, section 2Clause 2.He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he 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.