How to negotiate comp: moving from non-profit to PE

I currently work at an investor-focused non-profit, and am currently being recruited for an ESG-focused role at a large PE firm. I have demonstrated both strong subject-matter knowledge and an exceptionally strong network of senior execs from sovereign funds, pension funds, and other large asset owners that I have developed in 10+ years in an asset-owner facing role. I run a team of five and am responsible for c-suite and MD level relationships at large LPs. I started my career at a large asset management company before transitioning into economic policy and non-profit roles.

How can I go about evaluating what I should be paid if I take this role in a PE firm? I've been told I'll get carry and come in at a director level. I will have a ESG role, and I'm sure they'd like to tap my lucrative network to build deeper relationships and better position the firm. Client facing, responsible for building LP relationships. 

I have no idea how to value myself, but see this as a huge career opportunity. Any advice would be appreciated. Thanks!