The character of King Louie from The Jungle Book is not in this movie, because Disney would have had to pay the estate of voice actor Louis Prima had the character appeared in the film in any form.
Tony Jay portrayed Shere Kahn in this sequel. In The Jungle Book, George Sanders played the voice of Shere Kahn. George Sanders also happens to be Tony Jay's real name.
With the exceptions of King Louie the Orangutan, Winifred the Elephant (Colonel Hathi's mate), and the wolf pack, all the characters from The Jungle Book return in this sequel.
When Shanti goes to get water for the first time, and Mowgli and Ranjan sneak out to follow her, she seems to be humming the song that first lured Mowgli into the village in the first place: My Own Home.