The pomegranate tree represents Amir and Hassan's friendship and later when Hassan says that the tree no longer grows fruit it represents how their friendship and childhood innocence is lost. The pomegranate tree was always Amir and Hassan's hangout place where Amir would fully act like his friend ignoring the fact that Hassan was a Hazara, but this changes after the incident in the alley and Amir gradually begins to hold it against Hassan, and changes wanting to spend time with him. Hassan is loyal to Amir to a fault and when he smears the pomegranate juice on his own face, after Amir had thrown multiple pomegranates at him, it shows that he is still willing to be his friend even through all of the crappy things Amir has done to him. But towards the end when the tree no longer grows fruit it can also represent how Hassan is no longer loyal to Amir.
The tree represents the friendship that Amir and Hassan shared. When Amir first wrote the inscription onto the tree, their friendship was in its prime; Amir viewed Hassan as his friend, not just as a Hazara, and so the tree was abundant with fruit. When Amir and Hassan’s friendship was severed so abruptly and they never reconciled, the tree was bare of fruit.