The President does not have a security clearance, and thus there is no clearance to be pulled. The entire system of classified National Security Information in the US, the entire concept of a security clearance, exists purely by executive order. By default the President has access to any and all classified information, and it is the President who decides who should have access to that information. There is no one who can deny the President any information on national security concerns.
The top presidential candidates, once they've been nominated, receive security briefings, as a courtesy and as tradition. They began in 1952 under President Truman, who offered the security briefings to Republican candidate Dwight D. Eisenhower. Truman, who felt completely unprepared when he entered office in the middle of a war, believed no future president should be ignorant of intelligence matters. Truman had no clue about the Manhattan Project's bomb research until he was briefed the day after his inauguration.
They aren't the detailed daily briefings the President gets, but are once or twice a month, multi-hour, broad-picture briefings, usually given by the Director of National Intelligence (the first one for sure) or the Deputy Director. They are given at a mutually agreed upon time and secure location. George McGovern in 1972 never received any briefings because they could never work out a schedule to do so. Walter Mondale didn't think he was gonna win thus decided not to receive the briefings. But all other major party candidates have received the intelligence briefings.
The candidate's briefings are broad analysis, and do not get into the details of ways and means, or certainly not any planned covert operations. For example, if Hillary or Donald asks, "How did you learn that?" they won't get an answer. As President, they will definitely get the answer to the same question. The candidates aren't in the position of using the intelligence information to make executive decisions or policy, so the information is generally restricted and intelligence officials are likely to outline broad assessments about specific threats, like ISIS, China, Iran and Russia, etc., but they won’t get into sources or methods.
The briefings are mostly done to inform the candidates of the broad intelligence picture so they will know what they should and should not say on the campaign stump to avoid making global hot spots worse. Trump's musings about banning Muslims, dropping NATO commitments and leaving Japan and South Korea to mount their own nuclear defenses, puts him far outside of the U.S. foreign policy mainstream, so it will be interesting to note how his rhetoric and talking points change as he gets these briefings.
I've always found it fascinating to watch how the candidate's talking points can change a little, soften, or just up and mysteriously disappear once they start receiving briefings, and then sometimes are entirely reversed after they are elected and become the President. For example, remember when Obama campaigned hard about doing away with many of the Bush-era national security policies, many of which he was on record as being vocally in opposition to as a Senator, but he left many of those policies alone once he became President. One particularly glaring example is the closing of Gitmo and the abhorrent denial of habeas corpus rights of the Guantanamo detainees (enemy combatants). The last couple of months before the election he just kinda stopped talking about that. According to Project Vote Smart, a website that collects public statements by politicians, shows 21 instances where he mentioned it in press releases, stump speeches, media interviews and presidential debates, but stopped mentioning it altogether six weeks before the election, and the final two mentions prior to that were soft, general statements about looking into it closer.
Immediately after the election he began to signal a reversal of his stance on habeas corpus for the enemy combatants, and within four months of being elected he began appealing decisions by the U.S. District Court for the District of Columbia that have favored Guantánamo prisoners' petitions. At the appeals level, the Obama administration successfully persuaded the court to keep almost every Guantánamo petitioner in detainment. The court of appeals imposed legal standards that make it virtually impossible to win a habeas case at Gitmo. And the Supreme Court has refused to review the appellate court's rulings, signalling an end of meaningful judicial oversight of Guantanamo. And isn't that interesting.
That didn't happen as a result of reversed political rhetoric, because of some rare alignment of the stars that caused Obama and Bush to have the same position on such an unpopular and controversial issue, it happened because of what's in those intelligence briefings.