My sister who is an accomplished musician often performs at local jazz clubs.
Correct: A
The clause 'who is an accomplished musician' is a non-essential (or non-restrictive) clause; it provides additional information about 'my sister' but is not necessary to identify which sister is being discussed (since 'my sister' implicitly refers to a specific person). Non-essential clauses should be set off by commas. Option A correctly places commas before and after the clause.