In context: "By learning, in palestra, the virtues that pay off directly in competitive game,s the well-disciplined boy begins assembling the more abstract, gratification-delaying skills necessary for being a 'team-player' in a larger arena: the even more subtly diffracted moral chaos of full-service citizenship in a State."
Definition: I'll include two of the definitions:
1. In ancient Greece and Rome: a place devoted to the public teaching and practice of wrestling and other athletic exercises; a wrestling school, a gymnasium. hist.
2. In extended use: a place of combat, a battlefield; (also) a place to exercise one's intellectual skills, an arena for debate, etc.
Other: PALESTRA takes three back-hooks in Scrabble: ELS (PALESTRAE, PALESTRAL, PALESTRAS).
SNOOT score: 2
Source: Oxford English Dictionary