Even despite all their past differences, President-elect Trump has nominated South Carolina Governor Nikki Haley to be the the nation's next UN Ambassador and she has accepted. Once Haley's appointment to the cabinet position is approved by Senate, she will be bringing her nearly 12 years of domestic political experience to the international stage. Haley has never publicly expressed a desire to be UN Ambassador, but politicians and political experts alike have supported the idea of her running for president. In fall 2015, she expressed openness to the possibility of joining the GOP ticket as vice-president. As we all know, that didn't happen. However, depending on what the next four years have in store, the time may be ripe in 2020 for Haley's presidential bid. The biggest question then would be whether or not she would have to resign from her cabinet position to pursue the role that would give her a cabinet of her own.
There is some, though not much, precedent for this situation. Henry Cabot Lodge, Jr. left his post as UN Ambassador in 1960, after seven years of service, to run for vice president with Richard Nixon. (They lost.) President George H.W. Bush served as UN Ambassador from 1971 to 1973, but left the post years before joining Ronald Reagan's ticket as vice president in the 1980 presidential election. Daniel Moynihan, who served as the country's 12th UN ambassador, resigned from the position before running for and winning a seat in the Senate in 1976.
Hillary Clinton may provide the best example for Haley in this situation. Clinton, who first ran for president in 2008, waited until after serving as secretary of state before running for president for the second time this year. Still, there is no set rule that cabinet members must resign from their posts before starting a presidential campaign. Additionally, UN Ambassadors, like other cabinet members, can resign or be dismissed by the president at any time during their tenures. So if Haley challenges a Trump reelection race, the notoriously proud president-elect could just decide to fire her anyway.
Even so, the demands of a presidential cabinet position combined with the demands of running a presidential campaign could prove to be too much for even the most competent and experienced politicians. This is even truer when it comes to UN ambassadors, whose work can take them away from crucial campaigning time at a moment's notice.
Overall, if Haley doesn't want to just run for president in 2020, but win, she would most likely have to give up the UN ambassadorship to focus on running her campaign. The decision would all come down to which position she values most: serving under the U.S. president or becoming U.S. president (and the first woman to do so) herself.