'arch-conservative' is a compound formed in English from the prefix 'arch-' (from Greek 'arkhē'/'arkhos' meaning 'chief' or 'principal') + 'conservative' (from French/Latin roots meaning 'preserving').

'arch-' has been used in English since the late Middle Ages as an intensifying prefix (e.g. 'archbishop'); 'conservative' entered English in the early 19th century from French 'conservatif' and Latin 'conservare'. The compound 'arch-conservative' arose later as a descriptive intensifier of 'conservative'.

Initially, 'arch-' carried the sense 'principal' or 'chief'; combined with 'conservative' it came to mean 'extremely' or 'most strongly' conservative. The basic sense has remained an intensification of 'conservative'.