You can rewrite your query using a JOIN instead:
SELECT N.ID, N.NAME, TR.PUZZLE AS PUZZLE_OK, TR.PUZZLE_BIS AS PUZZLE_BIS_OK
FROM news N
JOIN puzzles TR ON TR.NID = N.ID
WHERE N.SERIESID = "1"
AND TR.TEAMID = "152"
Note that if it's possible no entry in puzzles exists for a given ID value from news, you should use a LEFT JOIN and move the WHERE condition on puzzles into the JOIN. This will then return NULL values for PUZZLE_OK and PUZZLE_BIS_OK in the same way as your subqueries will:
SELECT N.ID, N.NAME, TR.PUZZLE AS PUZZLE_OK, TR.PUZZLE_BIS AS PUZZLE_BIS_OK
FROM news N
LEFT JOIN puzzles TR ON TR.NID = N.ID AND TR.TEAMID = "152"
WHERE N.SERIESID = "1"
Note I've changed the alias on news to N to keep the SELECT clause consistent with what was in the subqueries in your question.