In the years after the victory at Endor the Rebel Alliance molds itself into the New Republic.
This era of Star Wars history is covered in the Expanded Universe, specifically the books under the "New Republic" banner, which cover the first twenty years after Endor.
Wookieepedia has a list.
Essentially, there are still battles to be fought, such as the taking of Coruscant in the second book of the X-Wing series, Wedges' Gamble. The closest person to the 3rd in command who takes control of the Empire after the deaths of Vader and Palpatine would be Ysanne Isard:
Ysanne Isard was a female Human who served as the Director of Imperial
Intelligence for several years during the Galactic Civil War, and
ruled the Galactic Empire herself for a time after the Emperor's death
in 4 ABY.
Other characters are shown leading the Empire (such as Paltr Carvin), but they don't last long.
After that in the first modern EU books (released in the early 90s) the Thrawn Trilogy by Timothy Zahn (set 9 years after Episode IV), Grand Admiral Thrawn takes control of the remnant of the Empire:
- Heir to the Empire
- Dark Force Rising
- The Last Command
(Also probably a good place to start with the EU)