I have only just started playing my first game of this and was wondering if there might be a stalemate situation if one player still had pieces but was unable to make a legal move.

I suspect that the only other way that a piece may stay on the board is if it is trapped between two opposing pieces on the edge of the board and a third piece moves to stop its movement away from the edge or a group of 4 (or more) pieces in a ectangular (square being on form thereof) cluster are trapped on all sides.