The tree of life is mentioned ten times in Scripture*: 7 times in the Old Testament (3 in Genesis, 4 in Proverbs), and 3 in the New Testament.
Gen 2:9 And out of the ground the LORD God made grow every tree that is pleasant to the sight, and good for food; the tree of life also in the midst of the garden, and the tree of knowledge of good and evil.
Gen 3:22 And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:
Gen 3:24 So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life.
Pro 3:18 She [wisdom] is a tree of life to them that lay hold upon her: and happy is every one that retains her.
Pro 11:30 The fruit of the righteous is a tree of life; and he that wins souls is wise.
Pro 13:12 Hope deferred makes the heart sick: but when the desire comes, it is a tree of life.
Pro 15:4 A wholesome tongue is a tree of life: but perverseness therein is a breach in the spirit.
Rev 2:7 He that has an ear, let him hear what the Spirit says unto the churches: To him who overcomes I will give to eat of the tree of life, which is in the midst of the paradise of God.
Rev 22:2 In the midst of the street of it, and on either side of the river, there was the tree of life, which bore twelve crops of fruits, and yielded her fruit every month: and the leaves of the tree were for the healing of the nations.
Rev 22:14 Blessed are they that do his commandments, that they may have right to the tree of life, and may enter in through the gates into the city.
The references in Genesis and Revelation discuss a tree, and are taken to mean something that God provides his people to preserve their life and health, along with their strength and vitality through the years. From the standpoint of these texts, it is another way of being like God.
The references in Proverbs take a different turn, and these things are also called a tree of life:
- wisdom
- the fruit of the righteous
- desire fulfilled
- wholesome speech
Based on the first of these where wisdom is called a tree of life, there is an ancient Jewish teaching that the tree of life in Genesis was wisdom, in contrast to the other tree with its knowledge. The book of Proverbs explores how wisdom does what the tree of life does, preserving life and health.
* As far as I have been able to determine. If there are other references I'd be glad to hear of them.