The Other is a being that inhabits the Macroverse. In the novel It, by Stephen King, the creature named It claims that The Other is the superior being in the Macroverse and although It and The Turtle are in eternal conflict, The Other is safe from this.
The Other never appears or is heard from in any novels in The Dark Tower Series or even It. It is very likely that The Other is perhaps Gan himself as the Turtle and It are both creatures of immense power and for a being to be superior to them would be a tremendous force, thus perhaps Gan. Other than that it could be a very powerful Todash Beast or perhaps even The Dark Tower itself (which is thought to be Gan too perhaps).