How to renew Israeli visa?: People who come to Palestine, get up to three months visa by the Israeli authorities upon their arrival. The Israeli government and its authorities are responsible for providing you with a visa either upon your arrival (the Palestinian Authority is not responsible as it does not control the state borders of Israel), or through its embassies/consulates prior to your visit.
Visas are routinely granted upon arrival at Ben Gurion Airport (Tel Aviv) if you are a citizen of an exempted country, or at the Allenby-King Hussein Bridge border crossing; Hamas controls the border in Gaza with Egypt. Tourist visas are valid for 90 days; most Americans and Europeans are issued three-month visas upon arrival and clearing customs.
Some people, specially who come to volunteer or doing an internship want to renew Israeli visa their stay to more than a three month and they wonder which way is the best to do so. Normally you have two options to re-new the Israeli visa, firstly; you can travel to Jordan as a visitor for couple of days where you get the chance to be in another country and discover its attractions. By crossing the border from Jordan to Palestine again, you will get a new tourism visa for a new three month.
In addition, you can also travel to Egypt and coming back in couple of days and renew Israeli visa as well. The other option is to extend the Israeli visa by the Ministry of Interior in Jarusalem at Shlom Tzion HaMalka Street in west Jarusalem but the possibility of obtaining a new visa is not high.
Therefore, it is recommended that you travel either to Jordan or Egypt and come back where you get a new tourism visa up to another three month.