Green’s Dictionary of Slang

(orig. US black) to pursue a goal or aim; to launch a career.

1967		P. Thomas Down These Mean Streets (1970) 97: I had the feeling that I was in a deep nothing and had to get on.
1983		R. Klein Jailhouse Jargon and Street Sl. [unpub. ms.].
2001		K. Sampson Outlaws (ms.) 8: Fuck knows why the Manc boys never got on it theirselves and that.
2005		B. Coleman Rakim Told Me 106: ‘It might seem like it is, hearing it today, but it's not Slick Rick influenced, because I wrote that before Rick got on’.
2014		C. Eble (ed.) UNC-CH Campus Sl. Spring 2014 7: GET ON IT — take action: ‘Almond pizza. Get on it, Lenoir’.