All I remember off the top of my head was the tree would alter the elderly people into a new form of protector. When we were exiled we were cut off from the tree and were forced to grow old and die instead
This is Protector by Larry Niven. Humans (originally a species called 'Pak') originated from a planet near the galactic core. Pak are born stupid as 'Breeders', but then as they grow older they instinctively eat the root of the "Tree of Life" which transforms them into super-intelligent, super-strong 'Protectors'. Protectors, as the name implies, protect the Breeders.
Humanity is descended from Pak who colonized Earth, only to find that Tree of Life wouldn't grow here, and modern humans evolved from Breeders.
I believe a Protector wouldn't die as long as they continued to eat Tree of Life root, so they were immortal (and very hard to kill on purpose).
Are you thinking of Larry Niven's Ringworld series?
There is an alien race called the Pak who were the ancestors of humans. They were the species Homo Habilis that evolved into modern humans.
When they get old they eat a plant called Tree-of-life that causes them to transform into a powerful and intelligent form called a Protector. Humans are also transformed by eating the plant but the form into which they are transformed is different from a Pak Protector, presumably due to the evolutionary changes humans underwent from the Pak/Homo Habilis.
It's a more tenuous link than the existing references to Niven's Ringworld series, but this also matches with James Rollins's Amazonia where Nathan Rand, heir to the Rand Corporation, enters into the Amazon in search of a miracle cure which has sprung up somewhere in the Amazon Rainforest in South America, especially important because a deadly plague is occurring in the world outside. The ultimate revelation is that there is a tree that is considered to be the source of all life, whose sap does indeed have tremendous curative properties, but also transformative ones, turning members of the tribe (and, as it turns out, Nathan's lost father) into its protectors, unable to live without access to that sap.