The commander of the Union forces was George Meade, but not all of the Union forces were Republican. Most of the Irish regiments, for example, were Democrats, as was Union cavalry George Armstrong Custer.
Lee for the South, Meade for the North
General Robert E. Lee was in command of the Confederate army at Gettysburg.
George G. Meade
General George Meade
Meade commanded the Army of the Potomac.
Lee for the South; Meade for the North…
The newly-promoted George Gordon Meade.
If you're referring to the President of the Confederacy while the Battle of Gettysburg was taking place, then it was Jefferson Davis.
Lee commanded the South. Meade commanded the North.
George Gordon Meade
George Picket
The Battle of Gettysburg was fought in Gettysburg, Pennsylvania.