A round pen is not strictly necessary for liberty training but is strongly recommended for beginners because its enclosed circular shape provides a contained environment that makes early communication much more accessible. The round pen's walls prevent the horse from moving indefinitely away from the trainer, which means early directional cues and the draw can be established without the horse having the option to leave entirely.
As liberty training progresses and the horse's responsiveness becomes reliable, the work can and should be transferred to larger spaces — a standard arena, a larger pen, eventually an open field — because a horse that will only work at liberty in a small enclosed space has learned compliance based on the enclosure rather than genuine responsiveness to the trainer.
The alternative to a round pen is a larger square or rectangular arena, which works well once the trainer has developed enough clarity and timing to compensate for the corners. Some practitioners work in very large spaces from the beginning, arguing that the constraint of the round pen creates dependency on the enclosure that must be un-trained later. For most trainers, however, the round pen provides an invaluable foundation environment for early liberty development.