Which movement of substances through a cell membrane against a concentration gradient requires energy?

The answer to this is active transport.

This is a kind of movement of substances. Unlike diffusion or osmosis, the substances move against the concentration gradient (ie. from low concentration to high concentration). This process requires extra energy generated such as from cellular respiration.

In addition, this process also requires a carrier protein, where it'll pick up certain substances that are needed to transport and move it to the other side. Some examples of movements of active transports are such as root hair cells of plants picking up minerals, or our small intestine absorbing nutrients digested.