President Biden, arriving in Israel in mid-July, will land in a country entering its fifth election process in three and a half years. A much messier situation might arise on the Palestinian side, where a long-awaited leadership succession battle is heating up, though it is unlikely to be decided by an election. 

Mr. Biden will likely attempt to avoid political interference as television ads, public debates, street rallies, and other staples of Israel’s robust democracy get in gear. The Palestinian contest will be mostly played out in back rooms and could well lead to a bloody civil war. 

After avoiding naming a successor for years, the 86-year old president of the Palestinian Authority, Mahmoud Abbas — a heavy smoker with a perennial heart condition — is now signaling that Hussein al-Sheikh could be his choice. A Fatah insider, Mr. Sheikh until recently was a relatively obscure lieutenant of Mr. Abbas.

According to the rules that established the Palestinian Authority, once Mr. Abbas leaves the scene the speaker of the parliament is to assume the presidency on an interim basis until an election can be held. The current speaker is a Hamas politician, Aziz Dweik. Mr. Abbas’s preferred successor could spark a bloody fight between Fatah and Hamas.

That fight might soon be out in the open. On June 5, the British Broadcasting Corporation’s Arabic service issued a tweet saying that Mr. Sheikh had started assuming some presidential duties with Mr. Abbas’s health deteriorating. Mr. Sheikh wasted no time in responding.

“There is no truth to the yellow news circulating about the health of #President #Abbas,” he tweeted. Rumors to the contrary are “an attempt at tampering with the internal #Palestinian situation,” he added. 

Yet, because dissatisfaction with Mr. Abbas’s leadership is more widespread than at any time since he assumed power back in January 2005, the staged retort from Ramallah, complete with a photo of the president working at his desk, failed to quell succession talks. Mr. Abbas is widely known to be in failing health.

“The institutional processes that had once existed to ensure a smooth transition of power are no longer viable,” a political analyst of Palestinian affairs, Omar Rahman, writes. “Public trust in governing institutions and the officials who lead them have suffered irreparable damage.” Mr. Abbas’s inevitable departure, Mr. Rahman wrote, “could result in fierce political infighting for control.”

Mr. Abbas was elected as successor to Yasser Arafat in a 2005 presidential contest at the West Bank and Gaza. His four-year presidential term was followed by a parliamentary election a year later that was won by Hamas, a terrorist organization rivaling Mr. Abbas’s Fatah party. 

A year after Israel forcefully removed all Jewish settlers and army troops from Gaza, Hamas chased all Fatah officials from the strip, using such tactics as tossing political rivals from high-rise rooftops, kneecapping Fatah bigwigs, and otherwise intimidating any would-be rival. 

Since then, Mr. Abbas has occasionally promised to conduct national elections, but he has never followed through. Last summer, after months of preparations for Ramallah’s resumption of the electoral process and cheers from around the world, the election was abruptly canceled. 

As in the past, Mr. Abbas cited as the pretext for canceling the election Israel’s refusal to allow Arab residents of East Jerusalem to participate. Meantime, as Mr. Abbas enters the 17th year of his four-year term, challenges are mounting. 

Some come from abroad. A former Fatah commander of Gaza, Mohammed Dahlan, has resided in the United Arab Emirates ever since escaping from the strip. From Abu Dhabi, where he became a top adviser to the UAE leadership, Mr. Dahlan is increasingly financing power centers in Gaza and the West Bank, in opposition to Mr. Abbas. 

Other challengers are from within Mr. Abbas’s own party, and even from inside the Ramallah seat of power, known as the Muqata. Last year a former Palestinian ambassador at the United Nations, Nasser al Kidwa, announced an independent presidential run. Mr. Abbas promptly ousted him from Fatah. 

Lacking any political following despite a dynastal legacy — Mr. al-Kidwa is Arafat’s nephew — the savvy former UN diplomat mounted a campaign with one of the most popular figures in Palestinian politics, Marwan Barghouti. According to polls, Mr. Barghouti is far more popular than Mr. Abbas. Yet his ability to lead is questionable, as Mr. Barghouti is serving a multiple life sentences in an Israeli prison for directing deadly terrorist attacks. 

In May, Mr. Abbas unilaterally promoted Mr. Sheikh to chairman of the Palestinian Liberation Organization. That position, held by Mr. Abbas prior to succeeding Arafat, is seen as a stepping stone to the presidency. Other Fatah leaders were left behind and uneasy. 

Along with the General Intelligence Service chief, Majid al-Faraj, Mr. Sheikh is now the leading power inside Mr. Abbas’s inner circle. The possibility remains that Mr. Faraj will marshal his security apparatus, as well as his tight relations in Washington and Jerusalem, to vie for the leadership. Once Mr. Abbas is gone, he could turn on Mr. Sheikh. 

The biggest danger looming over the succession battle, however, is Hamas’s growing popularity in the West Bank. Last month Hamas won in a landslide the election for the student board at Bir Zeit university near Ramallah. In lieu of national elections, the student poll is widely considered a bellwether of the public’s mood.

Hamas has built major West Bank power centers to complete its hold over Gaza. Its recent instigation of violence on Jerusalem’s Temple Mount has proved popular. Once Mr. Abbas is gone, a political power the State Department lists as a terrorist organization may well take the reins in Ramallah. Best for the White House would be if the potentially violent succession battle starts after Mr. Biden leaves the Mideast.