This mention of a palm tree seems to appear in the Septuagint version of the Book of Job, not the Masoretic text. The idea is of a life that is as long as a palm tree is tall, Job 29:18:
“And I said, My age shall continue as the stem of a palm-tree; I shall live a long while.”
KJV Job 29:18 –with some serious hysteron proteron going on– has:
“Then I said, I shall die in my nest, and I shall multiply my days as the sand.”
I like the palm tree as an image of a benign longevity, not just the height but the slender pliancy of the palm contributing to the image — (quite unlike the oak of War & Peace, to make a far flung reference, another tree associated with old age).
Reminds also a little of the Odyssey’s Delian palm, there the palm sapling associated with youth.
PLANTS 