English translation: postgraduate course in piano performance
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Wie vorgeschlagen habe ich den deutschen Begriff beibehalten und die englische Erklärung in Klammern hinzugefügt. Vielen Dank Euch allen für die rege Beteiligung! 4 KudoZ points were awarded for this answer
In the context of Musikhochschulen in Germany there is usually a differentiation between "künstlerische" and "pädagogische" Studiengänge for instrumentalists.
I'm being deliberately flippant here, so don't take this literally, but it's a bit on the line of "if you can, do; if you can't, teach".
Really good pianists, singers etc follow the "künstlerischen Studiengang" and become solists, i.e. they can make their living as performing musicians. As we all know, a minuscule proportion of those who start learning e.g. the piano...
Those who are not quite so good (as well as those who wanted to anyway) even if they are still brilliant players as far as the normal concert-goer can judge do the "pädagogischen Studiengang" and learn to teach either their instrument or school classes.
BTW the standard of musicianship in German school music teachers is high.
Thus the künstlerisches Aufbaustudium is a very high level course of study for someone who has already done the first diploma. As I say in my individual comments, "künstlerisch" has nothing to do with the Fine Arts here, but refers to the ability of the soloist to play as a "Künstler" , i.e. to give an "artistic" performance.
so that phrase makes it one clause, making the Aufbaustudium an extension of the degree course, just as orla suggested. Whether a Master's degree was the result I do not know as it does not feature in your post. So I'd probably just call it a postgraduate diploma for soloists.
I'm not sure how to translate it, but this is without any doubt nothing to do with the fine arts in general. It is instead a high level, postgraduate course for performing musicians.
If "Klavierausbildung" is synonymous with a degree program in Music, then I agree with orla's and Jonathan's use of (post)graduate. Combined with the valid question whether "kuenstlerisch" does indeed rather refer to another music program in this case, this appears to be a most context-heavy problem than I initially realized.
Künstlerisches Aufbaustudium - Künstlerische Fortbildung Orgel
Dieses Aufbaustudium mit einer Regelstudienzeit von zwei Semestern dient der Vertiefung der im vorangegangenen Studium erworbenen künstlerischen Fähigkeiten, Fertigkeiten und Kenntnisse. http://www.hfm-weimar.de/v1/studium/institute/fk3/schulmusik...
:-) is most probably right that this is a postgraduate course in music not fine art as it is used above for the orgel but as its not clear I would check - maybe she did go and do an art course!
The translation workplace 
peer agreement (net): -1