In post-Lovecraft stories, the Elder Gods oppose the Outer Gods and the Great Old Ones. Arthur Derleth attempted to retroactively group the benevolent deity Nodens in this category (who acts as deus ex machina for the protagonists in both "The Dream-Quest of Unknown Kadath" and "The Strange High House in the Mist").
As for Great Old Ones, Joseph S. Pulver mentions in his "Nightmare Disciples" (2006) a series of original Elder Gods, though lacking of any description about their true form. The story introduces entities as Adaedu, Alithlai Tyy, Dveahtehs, Eyroix, Ovytonv, Urthuvn, Xislanyx and Xuthyos-Sihb’Bz. Others have a cult title as Othkkartho (Sire of the Four Titans of Balance and Order), which is said to be Nodens's son, and Zehirete, who is The Pure and Holy Womb of Light. Sk’tai and Eppirfon are brothers and the former (female) has been Cthulhu's second bride who bore him a son, T'ith, now dead, murdered by Cthulhu himself.
Another Elder God with no description is Walter C. DeBill, Jr.'s Paighon, an extra-galactic entity which now dwells in Earth's core, said to be inimical of the Outer God Ngyr-Korath and its servitor Ymnar.