Old English -istre, from Proto-Germanic *-istrijon, feminine agent suffix used as the equivalent of masculine -ere (see -er (1)). Also used in Middle English to form nouns of action (meaning "a person who ...") without regard for gender.
The genderless agent noun use apparently was a broader application of the original feminine suffix, beginning in the north of England, but linguists disagree over whether this indicates female domination of weaving and baking trades, as represented in surnames such as Webster, Baxter, Brewster, etc. (though modern spinster probably carries an originally female ending). For Dempster, see deem (v.).
Also compare whitester "one who bleaches cloth;" kempster (c. 1400; Halliwell has it as kembster) "woman who cleans wool." Chaucer ("Merchant's Tale") has chidester "an angry woman" (the 17c. had scoldster). A c. 1400 psalter has yongling tabourester "girl drummer" (for Latin puellarum tympanistriarum). Also compare Middle English shepster (late 14c.) "dressmaker, female cutter-out," literally "shapester," sleestere (mid-15c.) "murderess, female killer" ("slay-ster"). Sewster "seamstress" (Middle English seuestre, late 13c. as a surname, also used of men) is still in Jonson but was obsolete or provincial after 17c.
In Modern English, the suffix has been productive in forming derivative nouns such as gamester (compare gamer), roadster, punster, rodster "angler," throwster "gambler," etc. But still with consciousness of sex; Thackeray (1850) has jocular spokester "female speaker or spokesman." Tonguester "talkative, loquacious person" seems to be a nonce-word (1871). "American Speech" in 1935 reported that "Singers are now tunesters to advertising writers for vaudeville and other entertainments."