I assume that ‘hierarchy’ was earlier pronounced /hie-/ rather than /hai(e)-/. Is this right? If so, when did the change occur?
The sound change in hierarchy is consistent with the Great Vowel Shift (c. 1400 - 1700), which lifted /i/ to /aɪ/.
Before the Great Vowel Shift, a series of vowel changes in English that occurred gradually between 1400 and 1700, vowel spelling was relatively consistent with pronunciation. (See the Wikipedia article for a general overview.)
According to the Middle English Dictionary, spellings of hierarchy in Middle English ranged from
iherarchie. The [g] and [j] are artifacts from Old French (Anglo-Norman Dictionary), whereas the [h] and [ie] preserve elements of the classical Latin spelling
hierarchia (Wiktionary). Most of the example quotations preserve the [ier] spelling.
As spelling began to standardize in the 16th and 17th centuries, English writers preferred the more classical Latin version with [hier]. The OED places the hier- spelling as from the 15th century on, and Early English Books Online (a database of early printed texts) has results for hierarchie from the 16th century. By the 17th century, it appears consistently in early lexicons and dictionaries. Hierarchie appears in A Table Alphabetical (1604) by Robert Cawdrey; hierarchy appears in A Christian Dictionary (1612) by Thomas Wilson.
If the lone [e] vowel had persisted from Middle English spellings, it might have shifted from /e/ to /i/. However, [ier] and [hier] as a form show up early enough (15th century) that hierarchy likely went from /i/ to /ai/, possibly with an intermediary step /әi/. Conventional resources on GVS state that /ai/ is well-established by about 1700, and I see no reason to except hierarchy from that explanation.