"eager ambition" is a correct and usable phrase in written English.
It refers to a strong and enthusiastic desire or drive to achieve something. You can use "eager ambition" to describe someone's determination and drive towards a goal or dream. For example, "Alice approached her studies with eager ambition, determined to excel in her chosen field of science." This conveys that Alice is highly motivated and determined to succeed in her academic pursuits.
"...It makes the prophet in us all presage The glory of a next Augustan age Of a power leading from its strength and pride, Of young ambition eager to be tried, Firm in our free beliefs without dismay, In any game the nations want to play.
In 1993 the leaders in sustainability were local authorities, many of them eager to implement the ambitions of Local Agenda 21 set out at the first Rio Earth Summit.
Mr. Cox, 34, a New York investment banker with political ambitions, was eager to bask in the celebratory glow of a Nixonian legacy uncomplicated by memories of Watergate and a resignation in disgrace.
Mr. Clavin, a man of obvious talent and ambition, is clearly eager to test the springs of the political platform once stood upon by Receiver of Taxes Alfonse D'Amato.
It also demonstrated how the blind ambition of an eager young student like Hal could make him incapable of recognizing someone else's genius if it did not come gift-wrapped in a man's body.
Whatever Hastings's ambitions, he was eager not to appear to be competing with his sources of content.
Many of the protest leaders have political ambitions and appear eager to leave Bangkok only with an unambiguous victory.
Jalal, who is starting to develop political ambitions, seemed especially eager to prove that he had solid reasons to hold onto his 12 prisoners.
And while Softbank may not yet be in control of Sprint, the Japanese company seems eager to embark on its ambitions in the United States.
Another reason that digital has become so prevalent is that it feeds the opening-weekend box-office ambitions of conglomerates eager to exploit comic-book-style filmmaking for teen audiences.
