It is not clear whether Elizabeth has any motivation for anything specific in Jane Austen's Pride and Prejudice. Her changes in the story are, as she says herself, "gradual". During the first part of the novel she seems to be driven by the desire of seeing Jane happily attached to Bingley. Then she moves on to analyzing the awkward behaviors of her family in public, and to pass judgement on people: Darcy is a proud man, Miss Bingley is a fake friend, Mr. Wickham is a poor, tortured man, and Mr. Collins is annoying. All these descriptors come from Elizabeth's perspective: She has very little motivation for anything, except finding herself through understanding others.
However, there is a moment in the novel when we see Elizabeth developing a curiosity and changing her view of Darcy. It is an interesting moment which also could reveal a hidden motivation embedded within the novel.
In chapter 43 we find Elizabeth visiting Pemberly, which is Darcy's estate, for the first time. Somehow, the visit to this massive, expensive, and gorgeous place "suddenly" eases out her dislike for Darcy. In fact, she even says that she could have been the mistress of it all! However, Austen cleverly disguises this tendency in women by pointing out that Lizzie also realized the good nature of Darcy when she heard his maid say great things about him. Yet, in Elizabeth's mind, the sight of Pemberly made a HUGE difference.
As for Elizabeth, her thoughts were at Pemberley this evening more than the last; and the evening, though as it passed it seemed long, was not long enough to determine her feelings toward one in that mansion, and she lay awake two whole hours endeavoring to make them out. She certainly did not hate him.
So, the question is:
Does Austen add the detail of Elizabeth's impression of Pemberley to convey some sort of indication that such are the tendencies of women? Is this Elizabeth's sudden motivation? We really will never know. However, the reality is that Austen does not allot Elizabeth much of a goal, except that of being herself, and remaining so for good.