What direction will the wind be shifting?

You answered: Counterclockwise

You've got it! "Wind backing, weather's lacking; Wind veering means clearing." The "Red sky at morning; Rider take warning" sky indicates that the sun is shining through dry, dusty air and clear skies to the east (which were ushered in by "veering" clockwise winds). That's your clue that the skies are about to cloud up, accompanied by a counter-clockwise ("backing") shift in the wind.