get on in the world or company, etc. Prosper or succeed, as in Her inheritance has helped her get on in society, or Dad asked if Bill was getting on in the company. [Early 1800s]
get on with it. Move ahead, pursue one's work. For example, We've spent enough time talking about it; now let's get on with it. [Early 1800s]
get on for. Advance toward an age, amount, time, and so on. For example, It's getting on for noon, so we'd better eat lunch. This usage is often put in the participial form,
getting on for. [Mid-1800]
See turn on, def. 3. Also see the subsequent entries beginning with get on.