"triumphant, flourishing," literally "worthy of the palm" (of victory or triumph), c. 1600, from palm (n.2) in the "triumph" sense + -y (2). The meaning "full of palms" attested from 1660s.
a palmy time for stockbrokers
palmar
palmer
palmetto
palmistry
palm-tree
palmy
Palmyra
palomino
palooka
palp
palpable