We were glad that by the time we got there the play ---yet

应该选择后者,即：hadn't begun hadn't begun 的完整形式应该是：had not begun,而 had not begun 是 has not begun 的过去式形式。has not begun 一般是完成时,表示现在已经做完的动作,题中的前一个选项 hasn't begun 就是这个。不过从这个题目可以看出,这是一个过去时的句子,所以要将 has 变成 had ,也就是说将现在完成时变成过去完成时。所以选择后者。