IGO worker transitioning into Consultancy (ESG / PPP), upcoming HSG-MIA

Business Chimps! Not so business chimp here trying to go into consultancy. 

My background is in (Bsc.) International Development, having interned at the UN and worked on international projects related to science, technology innovation, and economic development for the AU for 2 or so years now. 

Ive decided to go to HSG for the Masters of International Affairs and Governance, specialising in Climate Solutions and Development to get a greater practical background and a closer connection to industry/business (I also good a fullride). 

Nevermind that, but Ive been considering transitioning into industry/consultancy as Im not a big fan of IGOs, but Im currently struggling to find footing among the finance people, economists and so on given my diplomacy background, albeit having worked with industry at IGO level. 

Im looking towards positions either at consultancies or something like the World Economic Forum, but my question is: do you guys have any insider tips on how to fill the "business gap" so to say. WIth my background I dont think Im their general candidate, but how could I change that?

I decided to go to HSG instead of traditional policy schools (such as SciencePo, IHEID etc.) in hopes of getting a comparative advantages compared to those goobers, but in your experience, how the hell can someone like me hop on into consultancy? Do yall know of any consultancies that work within my field perhaps?

Thanks a bunch,