'archpresbytery' is formed from the prefix 'arch-' (from Greek 'arkhi-' meaning 'chief') + 'presbytery' (from Greek 'presbyterion' meaning 'place of a presbyter', via Latin 'presbyterium' and Old French/Medieval Latin).

'presbyterion' (Greek) → 'presbyterium' (Latin) → 'presbytery' (Middle English) and combined with the Greek/Latin-derived prefix 'arch-' to produce 'archpresbytery' in later English usage.

Originally indicated the 'place or office of a presbyter (elder)'; with the prefix 'arch-' it came to denote specifically the 'chief presbyter's office or jurisdiction', which is the modern meaning.