Suffixes are not words, but endings tagged on to words.
-tion
-ly
-ment
-ness
None of these mean anything by themselves; they are not discrete words.
specific is a word, an adjective. "Gender-specific" is a compound adjective, an adjective formed by combining two words (adj-adj, adj-noun, noun-verb)
Other examples:
age-old -- two adjectives
a ten-year mortgage - adj-noun
man-eating tiger - noun-verb