'an eagerness' is correct and usable in written English.
You can use 'an eagerness' when wanting to describe excitement or enthusiasm for something. For example: He had an eagerness to explore the new city.
Beyond an eagerness to please, impersonality is its signature quality.
They also often encounter an eagerness to resort to medication.
Demonstrate a willingness, even an eagerness, to learn.
— an eagerness perhaps not unmixed, at moments, with apprehension.
Rhythm, it goes without saying, but also glamour, a certain pizzazz, an eagerness to please.
Feliciano expressed an eagerness to make the Mets eat their words.
All you need is an Internet connection and an eagerness to learn.
What the museums all had, however, was an eagerness to challenge convention.
"Obviously, there was an eagerness here, so I was happy," Ms. Cahalan added.
Both will likely signal an eagerness to do the same in Afghanistan.
One manifestation of that ethos has been an eagerness to take on potentially exasperating public assignments.
