I will suggest two possible interpretations of this difficult concept. Firstly we must remember that a person whose honor was slighted especially publicly is considered as if he had died, since "one who embarrasses his friend publicly is akin to a murderer". If the person slighted overlooks his hurt and does not take revenge he receives a new lease on life, it is as if he is reborn.

The Gemara in Rosh Hashana 17a depicts this graphically, stating that even a person on his deathbed can recover fully if he was Maavir Al Midosav (overlooks slights from others) since all his sins are forgiven.

This "rebirth" process grants him new years which he didn't have before and therefore the Angel Of Death who has the extra years from those who lost them will transfer them to the person who overlooked his hurt and received "new" life.

The reason why this refers specifically to a rabbinical scholar is because there is an obligation to respect them, so when they are slighted it is both a terrible sin and also a big opportunity for them to waive the honor they deserve and receive new life in return.

The second possible explanation (based on the Chida's interpretation in Petach Eynayim) is that the person who died without trial still could have effectively reached much higher levels in his life and this ability was taken from him. However if his years are given to a rabbinical scholar who does not hold grudges, such a person will learn Torah for its own sake and not for self-aggrandizement and as he studies and grows the soul of the person who died will rise in tandem and get closer to Hash-m since effectively it is his years which are enabling the scholar to grow and purify himself through his Torah study.

Yoel Domb