There is no timeline on when the president must nominate a replacement.
Before the 25th Amendment, there was no procedure for selecting a replacement for the vice president. The assassination of President John F. Kennedy spurred the movement for the 25th Amendment.
History: Seven vice presidents have died in office: George Clinton who served under both Thomas Jefferson and James Madison; Elbridge Gerry who served under Madison; William R. King who served under Franklin Pierce; Henry Wilson who served under Ulysses Grant; Thomas Hendricks who served under Grover Cleveland; Garret Hobart who served under William McKinley; and James Sherman who served under William Howard Taft
When Harry Truman succeeded Franklin D. Roosevelt as president in 1945, the vice presidential office remained vacant for four years.
After the assassination of John F. Kennedy, there was no vice president from November 22, 1963 until Hubert Humphries' inauguration January 20, 1965.
July 6, 1965 - The 25th Amendment is sent to the states and is ratified on Feb. 10, 1967.
1973 - Gerald Ford becomes the first vice president chosen under the 25th Amendment after Vice President Spiro T. Agnew resigns.
1974 - After Richard Nixon resigns and Ford assumes the presidency, Ford nominates Nelson Rockefeller to be vice president.