Your letter is quite disjointed. Sentences seem thrown in randomly with little relationship to each other. You mention a group. What group? you mention she works in her field. What field? Don't assume the reader knows what's in your head.
You need to start out by introducing the student and mentioning what your relationship to her is in order to establish that you are qualified to comment on her performance. For example:
"It is my great pleasure to recommend the candidacy of Ms. Jane Smith for acceptance to your internship program. As her former music professor, I have known Ms. Smith for three years and am very familiar with her abilities and character."
Don't call her "the student" or "the applicant". They make the letter sound cold and distant, and perhaps like a form letter. The first time you mention her, use full name; use her surname afterwards (preceded my Ms. or Miss), or pronouns.
Only comment on things you have personally witnessed her doing. If you taught her classes, mention the names of the classes, the grades she received, and say something about her performance. Do not comment on classes you did not teach. A simple example:
"Ms. Smith attended my Music Theory class, in which she showed a strong grasp of the course material. She learned quickly, asked pointed questions, and exhibited an uncommon passion for the subject. Thanks to the intense interest she showed in class and her dedication to her studies, she succeeded in earning an A for the semester."
She's applying for an internship, it seems. Does the performance of her that you describe in your letter have any connection to the content of the internship?
Try to imagine you are the intended reader who knows nothing about your student. How would you introduce her and describe what you have seen her do, and how it would benefit them?