Сгенерировать список из генератора.
legal_moves = list(board.legal_moves)
Теперь список разрешенных ходов.
print(legal_moves)
[Move.from_uci('g1h3'), Move.from_uci('g1f3'), Move.from_uci('b1c3'),
Move.from_uci('b1a3'), Move.from_uci('h2h3'), Move.from_uci('g2g3'),
Move.from_uci('f2f3'), Move.from_uci('e2e3'), Move.from_uci('d2d3'),
Move.from_uci('c2c3'), Move.from_uci('b2b3'), Move.from_uci('a2a3'),
Move.from_uci('h2h4'), Move.from_uci('g2g4'), Move.from_uci('f2f4'),
Move.from_uci('e2e4'), Move.from_uci('d2d4'), Move.from_uci('c2c4'),
Move.from_uci('b2b4'), Move.from_uci('a2a4')]