The phrase "a second candidacy for" is correct and usable in written English.
It can be used when discussing someone's attempt to run for a position or office for the second time.
Example: "After a successful first campaign, she announced a second candidacy for the mayoral position."
Alternatives: "a second run for" or "a second bid for".
(Of course, had the Constitution permitted a third candidacy for Bill Clinton -- who, it is implied, deprived the Oval Office of integrity -- he would have won easily).
On 12 April, Hillary Rodham Clinton declared her second candidacy for president, this time as the Democratic Party favorite, supported by a large majority of Democratic-leaning voters.
In building his third candidacy for the presidency, he cobbled together an odd group of allies, some with contradictory visions.
John McCain, the United States Senator from Arizona, launched his first candidacy for the presidency of the United States in the 2000 presidential election.
In 1968, running a third-party candidacy for the presidency, the former Democratic governor of Alabama, George Wallace, campaigned with the veneer of race and violence ever present.
Before the accusations, Mr. Powell had been raising money for a possible second candidacy against Representative Charles B. Rangel, the dean of the New York delegation in Congress.
Others also seemed primed for a third-party candidacy.
In the last election, Mr. Bloomberg, the nation's most prominent and wealthiest independent elected official, explored the possibility of a presidential run but concluded that the moment was not right for a third-party candidacy.
But given the major differences between the prospective Democratic and Republican nominees, there is no driving logic for a third-party candidacy this year, and the public deserves to see the major-party candidates compete on an uncluttered playing field.
Even as he has issued denials of interest to everyone from the press corps at City Hall to Ryan Seacrest on Dick Clark's New Year's Eve broadcast, Bloomberg has deputized some of his leading aides to draw up scenarios for a third-party candidacy and to keep the interest of the press well fluffed.
