There are several synonyms for the word "galloping". One of the commonly used alternatives is "cantering" which refers to a medium-fast gait that involves three beats. Other synonyms include "trotting" which is a rhythmic two-beat gait, "running" which suggests a faster speed than galloping, and "bounding" which emphasizes the energetic and bouncy nature of the movement. For a more formal word, "hastening" can be used to describe a quick gallop. On the other hand, "prancing" and "skipping" are more playful and light-hearted options that are often associated with horses' movements.