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. Joining The Australia Institute staff in 2014, he became Executive Director in 2015.
Oquist began working with the Australian Greens in 1996 for both Dee Margetts and Bob Brown. Brown has described Oquist as a "friend and confidant" but also as "a core factor in the Greens becoming the third largest party in Australian politics". In a 2014 radio interview Brown stated that Oquist's approach to strategy aligned with that of his own. Oquist was reported to have been favoured by Brown for preselection as Greens senator for NSW in 2003. Upon the resignation of Senator Bob Brown on 13 April 2012, Oquist became chief of staff for the new leader, Christine Milne. In September 2013, Oquist was implicated in an attempt to unseat the then leader of the Australian Greens, Christine Milne. It was reported that Oquist was motivated to attempt to remove Milne before she restructured the organisation to remove his influence. Senator Milne had described him as an adherent to a hierarchical administrative structure, citing this as the reason behind his subsequent departure from his role on the Greens staff. His subsequent commencement with the Australia Institute aligned him with the economist and then Executive Director of the Australia Institute Richard Denniss. Denniss was also an outspoken critic of Christine Milne and a former Australian Greens staffer. Oquist was widely sourced for comment on the occasion of the resignation of Christine Milne as leader of the Australian Greens in May 2015, where he praised her role as a climate leader.
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. The meeting was instrumental in a deal brokered between the leader of the Palmer United Party, Clive Palmer, and the federal government of Australia for the concessional repeal of the carbon tax. 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. Following the demise of the Palmer United Party senate voting block in 2014 the deal collapsed. However, the newly constituted Senate crossbench did not vote to repeal the RET. The Carbon Pricing Scheme was abolished on 17 July 2014. Oquist's role in these events remains controversial as Palmer stood to benefit financially from the repeal through his ownership of a coal refinery.
