別のテーブルの列を更新する挿入トリガー後のmysql

これを試してください：

DELIMITER $$
CREATE TRIGGER occupy_trig
AFTER INSERT ON `OccupiedRoom` FOR EACH ROW
begin
       DECLARE id_exists Boolean;
       -- Check BookingRequest table
       SELECT 1
       INTO @id_exists
       FROM BookingRequest
       WHERE BookingRequest.idRequest= NEW.idRequest;

       IF @id_exists = 1
       THEN
           UPDATE BookingRequest
           SET status = '1'
           WHERE idRequest = NEW.idRequest;
        END IF;
END;
$$
DELIMITER ;