'clerically' ultimately originates from Greek via Latin and Old English: from Greek 'klērikos' (related to 'klēros'), through Latin 'clericus' and Old English 'clerc'/'clerk', and formed into English adjective 'clerical' + adverbial suffix '-ly'.

'clerically' developed from the adjective 'clerical' (Late Middle English), which came from Medieval Latin 'clericalis' and Latin 'clericus' (meaning 'clergyman'); Old English 'clerc/cleric' shifted in spelling and sense to modern 'clerk' and 'clerical' retained both religious and office-related senses.

Initially it meant 'in a manner of the clergy' (religious). Over time, because clergy historically performed administrative/writing tasks, the meaning broadened to include 'in an office/administrative manner'; both senses persist in modern usage.