A regular customer — someone who frequently visits the same shop, bar, or business.
あの居酒屋には常に数人のなじみ客がいる。
That izakaya always has a few regulars.
店主はなじみ客の好みをよく覚えている。
The owner remembers the preferences of his regular customers well.
常連のなじみ客には少し割引をすることがある。
Regulars sometimes receive a small discount.
A client who repeatedly visits the same prostitute or sex-worker (industry/slang term). This usage can be explicit and context-sensitive.
歓楽街では店に『なじみ客』がついていることが多い。
In entertainment districts, shops often have regular clients.
その店のなじみ客は顔を覚えられて特別扱いされていた。
The shop's regular clients were recognized and given special treatment.