The energy-requiring process by which a cell expels wastes and secretes substances at the plasma membrane is known as active transport. More specifically, the expulsion of waste materials and the secretion of substances often occur via a process called exocytosis.
Exocytosis involves the fusion of vesicles containing waste or secretory materials with the plasma membrane, leading to the release of their contents outside the cell. This process requires energy, typically in the form of ATP, because it involves moving materials against their concentration gradient or requires the membranes to fuse.
In summary, the process you are referring to is exocytosis, a type of active transport.