'pro-monarchically' originates from a combination of Latin-derived prefix 'pro-' (from Latin 'pro', meaning 'for') and 'monarch' (from Greek 'monarchos', meaning 'sole ruler'), plus the English adverbial suffix '-ically'.

'monarch' comes from Greek 'monarchos' → Latin/Old French adoption → Middle English 'monarch' and combined with English prefix 'pro-' to form pro-monarch- + adverbial suffix '-ically', producing 'pro-monarchically' in modern English.

Initially, the parts meant 'for' (pro-) and 'sole ruler' (monarchos); combined in modern English they mean 'in favor of monarchy' as an adverbial description.