Which appurtenance is used to denote a subsequent award?

The use of oak leaf clusters serves as a recognized method in military awards and decorations to signify subsequent awards for the same achievement. When a service member receives an award, such as a commendation medal, they may later receive additional recognitions for further distinguished service. The oak leaf cluster is added to the medal's ribbon, visually indicating that the service member has achieved this award more than once, without the need to issue a new medal for each award. This system simplifies the representation of a soldier's achievements while ensuring that their accolades are easily identifiable to others.

While clasps, service stars, and numerals can also represent subsequent achievements in certain contexts, they are associated with different awards and systems. Thus, oak leaf clusters are preferred for this purpose in the military award system, making them the correct answer in this instance.