In Spanish politics, the prime minister is officially known as "President of the Government", so, although rarely used due to Spain being a parliamentary monarchy, the term "presidential transition" it would be more appropriate.
[1][2] As a summary, the procedure is as follows: after a general election, the Congress of Deputies nominates a prime minister, who is subsequently appointed by the monarch.
The outgoing prime minister not presenting for re-election remains in office in a caretaker capacity until their successor is sworn in.
An example of this was the 2011 general election, when outgoing president José Luis Rodríguez Zapatero did not run for re-election and he took care of the office until the newly appointed prime minister, Mariano Rajoy, was sworn in.
[7][8] The term "prime minister-elected" is not proper to the parliamentary system because the president is not elected directly by the people but for the Congress.