'locally-banned' is an English compound formed from the adverb 'locally' (from 'local' + suffix '-ly') and the past participle 'banned' (from the verb 'ban').

'local' comes from Latin 'localis' (from 'locus' meaning 'place') via French/Latin medieval usage; 'ban' as a verb and noun goes back to Old English 'bannan'/'bann' (with related forms in Old Norse), later developing into the Middle English 'ban(n)en' and modern English 'ban'. The compound construction combining an adverb with a past participle (e.g., 'locally banned') is a modern English pattern.

The individual parts kept their basic senses: 'local' related to place, and 'ban' meaning to prohibit. Combined, they straightforwardly mean 'prohibited in a particular place'; the compound's meaning is a transparent extension rather than a major semantic shift.