Riyadh is part of a US-led coalition carrying out air strikes against Islamic State group militants in Syria and Iraq, and experts say the strategic alliance is likely to continue.
"I see the general contours of US-Saudi relations, particularly against IS, as remaining fairly solid," said Frederic Wehrey, a Gulf expert at the US-based Carnegie Endowment for International Peace.
Members of the Al-Saud dynasty "share the same world view but may differ slightly over matters of strategy and tactics," he added.
Following Abdullah's death on Friday, his half-brother Salman, 79, took control of the oil-rich kingdom.
Kuwaiti analyst Ayed al-Manaa said he expects Salman to maintain a "pragmatic relationship" with the West, despite growing signs of US and European rapprochement with Saudi Arabia's regional arch-foe Iran.
SUSPICIOUS OF IRAN
Ties between Riyadh and the West have long been close owing to mutual interests including oil and a tough stance on radical Islam, although they have slackened in recent years because of signs of an improvement in US-Iranian relations, according to Manaa.
Riyadh accuses Shiite Iran of interfering with the internal affairs of several countries, including Iraq and Syria but also neighbouring Bahrain and Yemen.
Manaa said Saudi Arabia "will remain wary" of Iran, which it suspects of supporting Shiite Huthi fighters whose deadly standoff with authorities in Yemen prompted President Abdrabuh Mansur Hadi to tender his resignation on Thursday.
Yemeni political sources say Riyadh may have already suspended aid to its southern neighbour over possible Iranian links to Huthis.
"Saudi pressures are expected to continue until the Huthis prove they are not serving as a bridgehead for Iran in Yemen," said Manaa.
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Other regular beneficiaries of Saudi aid may have to look elsewhere for foreign funding, according to Wehrey, as the kingdom tightens its belt following a sharp drop in oil prices.
The OPEC member derives 90 percent of its revenues from oil and could be forced to reduce its largesse to states such as Egypt, which Riyadh has supported politically and financially since the army ousted Islamist president Mohamed Morsi in July 2013.
"We are already seeing a curtailment of Saudi aid to Egypt and some moves to pressure (Egyptian President Abdel Fattah) al-Sisi to make subsidy reforms since the Saudis can't sustain the aid indefinitely with the declining price of oil," Wehrey said.
DOMESTIC REFORM UNLIKELY
Rapid change is also unlikely at home, analysts said, with Salman seen as supportive of policies implemented under his predecessor.
"Salman is known to be a conservative (and) he will find it difficult to adopt a policy away from that which was drawn by King Abdullah," Manaa said.
The country has witnessed several domestic militant attacks in recent years and analysts said King Abdullah's policy of providing aid to poorer segments of society must continue in order to head off a greater homegrown threat.
Despite its vast oil wealth, inequality remains widespread in the kingdom, and distributing funds to poorer residents -- "from whom Islamist extremists tend to recruit", is likely to continue under Salman, Manaa said.
Greater pressure for reform could come from Prince Moqren, who was named last March as second in line to the throne and on Friday replaced Salman as crown prince, experts said.
Moqren "could develop (the all-appointed advisory body) Shura Council so it evolves into a sort of parliament but with limited powers," said Manaa.
Wehrey agreed that the rise of the 69-year-old Moqren "may mark the start of a more accelerated reform programme at home".
He added, however, that such a programme was unlikely under Salman.
"I don't see any real shifts... until we start Moqren's tenure," Wehrey said.