"举行职业演奏会" can be translated into English as "hold a professional recital" or "stage a professional concert", depending on the context and the specific type of performance.
"Hold a professional recital" is more suitable when referring to a solo or small-group performance, often in a more intimate or specialized setting, like a classical music recital.
"Stage a professional concert" is a broader term that can encompass various types of musical performances, from solo acts to full orchestras, and is more commonly used in a general or promotional context.
Choose the phrase that best fits the specific situation and tone you want to convey.