How eager she was to do her best type of clause?

The phrase "eager she was to do her best" is a subordinate clause, specifically an adverbial clause.

Here's a breakdown:

* Subordinate Clause: A clause that cannot stand alone as a complete sentence and depends on a main clause for its meaning.

* Adverbial Clause: A subordinate clause that modifies a verb, adjective, or another adverb, providing information about time, place, manner, reason, etc.

In this case, the clause modifies the adjective "eager" by telling us how eager she was. It provides information about the degree of her eagerness.

Here's an example of how the clause might be used in a sentence:

> Eager she was to do her best, she practiced tirelessly for the competition.