The verb form in the present perfect is has wanted.
She wanted to start learning the violin at some point in the past, and still does to this day. She hasn't started yet, hence her still wanting to learn the violin.
The present perfect is formed by have + past participle.
It's used, amongst other things, to refer to an action in the present that started in the past and is still relevant to the present.
For example,
I have lived in London for 4 years. I moved to London for years ago and I still live London.
The overall tense is of course a present tense (as opposed to past, future or conditional).
Propel are confusing present tense with present simple. In English, there are four main tenses that are used to describe things in the present: present simple, present perfect, present continuous (also called present progressive) and the present perfect continuous.