We don't have synonyms for palestra yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are palaestra, balestra and maestra.
(n) :
(American spelling, uncommon) Alternative spelling of palaestra. [(historical) A public area in ancient Greece and Rome dedicated to the teaching and practice of wrestling and other sports; a wrestling school, a gymnasium.]
(n) :
(American spelling, uncommon) Alternative spelling of palaestra. [(historical) A public area in ancient Greece and Rome dedicated to the teaching and practice of wrestling and other sports; a wrestling school, a gymnasium.]