konjanik

1. horseman; rider
   Kroz selo je projahao konjanik u crnom kaputu. — A horseman in a black coat rode through the village.
2. (in the army) cavalryman; mounted soldier
   Na slici su prikazani srpski konjanici u bici. — The painting shows Serbian cavalrymen in battle.

A sports rider is usually called "jahač"; "konjanik" is more typical in historical and military contexts.