The sentence "she applied herself" is correct and usable in written English.
You can use it when you want to describe someone taking initiative to do something, or to describe someone showing dedication or effort in what they are doing. For example: "Sally was determined to learn how to play the piano, so she applied herself and practiced every day."
Whatever genre I gave her, she applied herself.
As she applied herself to very slow, dreamy renditions of "Misty," "Poor Butterfly" and "Someone to Watch Over Me," Ms. Callaway led you into the peach grove.
Gone was her signature showpiece, "Glitter and Be Gay," from "Candide," replaced by seldom-heard dramatic theater songs to which she applied herself with care and subtlety.
Many will remember her for the intensity with which she applied herself in various Upper Westside gyms over the years, exercising, spinning, and ultimately daily yoga.
But she applied herself to her work with formidable energy and passion and continued to reflect on how faith and politics related to one another.
She applied herself to the study of stem cells with fanatical devotion, and still found time to attend Harvard seminars on a huge range of topics.
She applies herself to this purpose with unflagging energy.
But once their sessions begin, she applies herself with intense dedication, asking how this or that feels.
She's a very determined person and cares hugely about what she does and brings a restless energy to what she applies herself to".
She begins another possible relationship with Ned (Keith Leonard), a recovering alcoholic who runs a stable, and as she curries his horses, she applies herself with a touching, maternal tenderness.
She has a task and she applies herself to it soberly: the trapping, if only in a mirrored surface, of some fragment of reality that might yield a truth about the whole.
