The stage of relatively rapid eruption from the time a tooth first penetrates the gingiva until it reaches the occlusal level is called :

Once a tooth emerges into the mouth, it erupts rapidly until it approaches the occlusal level and is subjected to the forces of mastication. At that point, its eruption slows and then as it reaches the occlusal level of other teeth and is in complete function, eruption all but halts. The stage of relatively rapid eruption from the time a tooth first penetrates the gingiva until it reaches the occlusal level is called the postemergent spurt, in contrast to the following phase of very slow eruption, termed the juvenile occlusal equilibrium. Contemporary orthodontics, Proffit WR, Fields Jr HW, Sarver DM. 4th edition, Page 90