Green’s Dictionary of Slang

1. (US drugs) an addict who volunteers themselves for a cure, taken in prison or a similar institution.

1936		D. Maurer ‘Argot of the Und. Narcotic Addict’ Pt 1 AS XI:2 126/1: self-starter. An addict who voluntarily places himself in an institution where he hopes to kick the habit.
1959		J.E. Schmidt Narcotics Lingo and Lore.

2. one who acts, esp. when employed, on their own initiative rather than await instructions or orders.

1960		Times 1 Feb. 2/4: [advert] The Man: Must be a self-starter yet able to work within references given to him.
1971		Sun. Times (Johannesburg) 28 Mar. 30/4: [advert] Suitable applicants will be self-starters in the 24–35 year age group.