Rank adjectives are listed in this post. Each word below can often be found in front of the noun rank in the same sentence. This reference page can help answer the question what are some adjectives commonly used for describing RANK.
above, academic, actual, additional, ambassadorial, ancient, apparent, appropriate, aristocratic, average, best, better, brevet, canonical, certain, chief, civil, clerical, close, commissioned, common, comparative, considerable, conspicuous, consular, corresponding, current, definite, different, diplomatic, distinguished, divine
double, ducal, due, e, earthly, ecclesiastical, elevated, eminent, enlisted, enough, episcopal, equal, equestrian, equivalent, exact, exalted, external, fifth, final, finite, first, foremost, formal, former, fourth, front, full, future, general, generic, good, great
greater, greatest, hereditary, hierarchical, high, higher, highest, honorable, honorary, honourable, human, humble, humbler, humblest, illustrious, imperial, important, independent, inferior, intellectual, intermediate, junior, just, kingly, knightly, last, latter, leading, less, lesser, like, literary
little, local, lofty, long, low, lower, lowest, lowly, mean, meaner, meanest, mere, middle, middling, military, ministerial, modest, moral, more, most, much, national, natural, naval, new, next, noble, nominal, numerical, official, old, only
ordinary, original, other, own, particular, patrician, permanent, personal, plebeian, political, possible, praetorian, precise, present, pretty, previous, priestly, princely, professional, professorial, prominent, proper, real, rear, relative, respectable, respective, rightful, royal, same, scientific, second
secondary, senatorial, senior, serried, similar, single, sixth, social, sovereign, special, specific, spiritual, star, subordinate, such, sufficient, suitable, superior, supreme, temporary, third, titular, top, true, unequal, university, upper, various, very, whole, worldly
Hope this word list had the adjective used with rank you were looking for. Additional describing words / adjectives that describe / adjectives of various nouns can be found in the other pages on this website.