Source : Webster's Revised Unabridged Dictionary (1913)

Riding \Rid"ing\, a.
   1. Employed to travel; traveling; as, a riding clerk. ``One
      riding apparitor.'' --Ayliffe.

   2. Used for riding on; as, a riding horse.

   3. Used for riding, or when riding; devoted to riding; as, a
      riding whip; a riding habit; a riding day.

   {Riding clerk}.
      (a) A clerk who traveled for a commercial house. [Obs.
          Eng.]
      (b) One of the ``six clerks'' formerly attached to the
          English Court of Chancery.

   {Riding hood}.
      (a) A hood formerly worn by women when riding.
      (b) A kind of cloak with a hood.

   {Riding master}, an instructor in horsemanship.

   {Riding rhyme} (Pros.), the meter of five accents, with
      couplet rhyme; -- probably so called from the mounted
      pilgrims described in the Canterbury Tales. --Dr. Guest.

   {Riding school}, a school or place where the art of riding is
      taught.

Source : WordNet®

riding master
     n : someone who teaches horsemanship