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For those wondering. Chapter III, Article 65 of the Constitution of the Republic of Korea clause 2 indicates that the Nation Assembly must have a simple majority to bring about impeachment charges and, for the President, a two-thirds vote to be convicted.
That a motion for the impeachment of the President shall be proposed by a majority of the total members of the National Assembly and approved by two thirds or more of the total members of the National Assembly
Clause 3 then indicates that once someone is impeached the impeachment is adjudicated.
Any person against whom a motion for impeachment has been passed shall be suspended from exercising his power until the impeachment has been adjudicated
Chapter VI, Article 111 Clause 1(2) indicates that the Constitutional Court will have original jurisdiction over adjudicating impeachments.
The Constitutional Court shall have jurisdiction over the following matters: 2. Impeachment
The National Assembly impeached Yoon Suk Yeol on December 14th, 2024. Prime Minister Han Duck-soo took over as acting President until his impeachment on December 27th, 2024. First Deputy Prime Minister Choi Sang-mok then took over as acting President until the Constitutional Court acquitted Han Duck-soo who then resumed as acting President.
Yoon Suk Yeol's impeachment was upheld by the Constitutional Court by a vote of 8-0. It is this ruling that the story linked is indicating.
Chapter IV, Article 68 Clause 2 indicates that when a permanent vacancy occurs in the office of the President, a new election must be held within 60 days.
In case a vacancy occurs in the office of the President or the President-elect dies, or is disqualified by a court ruling or for any other reason, a successor shall be elected within sixty days
So a new election will be held no later than June 3rd of this year. This will be to elect a new President to a single term of five years.