"rising ambitions" is correct and usable in written English.
For example, you could use it in a sentence like this: "John has always had rising ambitions to climb the corporate ladder."
Gould, a Harvard paleontologist and a popular-science writer, who died in 2002, was taking aim mainly at the rising ambitions of sociobiology.
Toutiao, which says it uses complex algorithms to decide what its users see, combines China's hunger for media content with its rising ambitions in artificial intelligence.
If 2012 was the year that unearthed unprecedented detail about corruption in reform-era China, 2013 may be turning the spotlight on the P.L.A.'s rapidly rising ambitions and capabilities.
And the rising ambitions of these eastern nations in Africa have spurred the Americans into action, anxious not to be outdone in a continent which they feel should be in their orbit.
And it is an enthusiastic joiner of international groups.On a shoestringAll this speaks of rising ambitions, even if most foreign-affairs experts wisely eschew any talk of an incipient superpower.
In terms of its military presence, Russia has rivaled the United States in recent years, launching major operations in Ukraine and Syria and having rising ambitions in the Arctic.
Many companies in Hong Kong said it was hard to find qualified candidates and complained that salaries were rising, Ambition said in another report.
At first, a lot of them were quite chuffed by the sight of turmoil in Iran, since they have long felt edgy about their big neighbour's rising ambition and influence in the region.
The group's budget, disclosed by a conference attendee, reflects the rising ambition and expanded reach of the Koch operation, which has sought to distinguish itself from other outside groups by emphasizing the role of donors over consultants and political operatives.
It takes Pete's youth mixed with his insecurity and rising ambition to change the course of the conversation.
On Friday, Politico editor Susan Glasser touted several recent hires and said the company is going through a period of "growth and rising ambition".
