The Next Generation
He could see the characteristics of their predecessors in them the moment he saw them. It wasn't just the physical characteristics (though they were the most obvious), but the psychological ones as well.
Naruto had the fierce determination of his mother, and if you looked close enough, his fathers supposed brilliance.
Sasuke was driven towards a single goal, and upon closer inspection, a caring heart, reminding Kakashi of another Uchiha.
And the girl Sakura . . . There was something about her too. She obviously cared deeply for others, and there was no way she was going down without a fight.
Over the years he would watch them grow, leaving the shadows of what he had seen in them behind and defining their own paths. They were still driven, determined, caring and fighters, but their legacy became their own.
Naruto decided his purpose was to protect everyone, no matter the toll on himself.
Sasuke achieved his goal and found a new one, to change the world.
And Sakura, She found her own purpose as well. Hers seemed cliché but it had value. She would be the one to support her teammates in their goals.