From Teflpedia

Elocution (/eləkju:ʃən/) is study of formal speaking in pronunciation, grammar, style, and tone.

Native English speakers may take elocution lessons in prestige accents (e.g. received pronunciation), standard English, style, rhetoric, etc. Students are often motivated by a desire not to be victims of othering.

Obviously there are transferable skills from teaching English as a foreign language to teaching aspects of English to native speakers.