Which term describes something that is self-serving or appropriate to a purpose?

The term that describes something self-serving or appropriate to a purpose is "expedient." This word often relates to actions or decisions that are advantageous or practical, even if they may not be the most ethical or moral choice. In contexts where individuals or organizations are aiming to achieve an outcome, "expedient" refers to a course of action that is convenient and serves their immediate interests or goals effectively.

In contrast, the other terms have different meanings. "Extempore" relates to something done without preparation, "exculpate" means to clear someone from blame or fault, and "exscind" refers to cutting out or removing something. Each of these terms does not capture the essence of being self-serving or relevant to a specific purpose, which is precisely what makes "expedient" the correct choice.