Oquist was (2015 to 2022) the Executive Director of The Australia Institute, an independent Australian think tank conducting public policy research on a range of economic, social, transparency and environmental issues.

[9] A 15-year career with Greens leader Bob Brown was broken briefly by a two-year stint with the public affairs company Essential Media Communications.

[17][18] In July 2014 Oquist, at that time a strategy director of The Australia Institute, was named as a party to the meeting between former US Democratic presidential candidate Al Gore and Clive Palmer.

[20] Oquist's role in the context of the repeal was widely reported to be one of pragmatism, driven by a focus on gaining support in particular for the mandated Renewable Energy Target which in 2014 was thought to be under imminent threat.

Oquist's role in these events remains controversial as Palmer stood to benefit financially from the repeal through his ownership of a coal refinery.