Elfrida Clagg was the Chieftainess of Warlock’s Council (JKR).
* The dates given on Clagg’s Chocolate Frog card (1612-1687) conflict with information from QA4 which says she was the “Chief of the Wizard’s Council” in the mid-1300s.
During a Wizards’ Council summit on the Classification of beasts and beings, she attempted to define “Beings” as creatures who could communicate with the Wizards’ Council using human speech. Unfortunately, this meant that Trolls who had been taught a few words, wild Jarveys and ghostly “non-beings” were included, but the Merpeople who could not speak unless above the water were excluded (FB).
Elfrida is a variant spelling of the Old English name Elfreda (Ælfþryð), meaning "elf strength" (Behind the Name).
Clagg may derive from the surname Clegg, which is a locational English name from the Old Norse kleggi ("haystack") (Internet Surname Database).
Clagg was the "Wizard of the Month" for June 2005 on Rowling's website (JKR).
Unless there were two Elfrida Claggs, the fourteenth and seventeenth century dates are very hard to reconcile.