1510s, "a composition presenting in dialogue a course of human action, the description of a story converted into the action of a play," from Late Latin drama "play, drama," from Greek drama (genitive dramatos) "action, deed; play, spectacle," from drāo "to do, make, act, perform" (especially some great deed, whether good or bad), which is of uncertain etymology.
Meaning "theatrical literature generally, drama as art" is from 1660s. Extended sense of "sequence of events or actions leading up to a climax" is by 1714. Drama queen "person who habitually responds to situations in a melodramatic way" is attested by 1992.
word-forming element meaning "one who does or makes," also used to indicate adherence to a certain doctrine or custom, from French -iste and directly from Latin -ista (source also of Spanish, Portuguese, Italian -ista), from Greek agent-noun ending -istes, which is from -is-, ending of the stem of verbs in -izein, + agential suffix -tes.
Variant -ister (as in chorister, barrister) is from Old French -istre, on false analogy of ministre. Variant -ista is from Spanish, popularized in American English 1970s by names of Latin-American revolutionary movements.