There is a fairly low level of awareness of the causes and effects of climate change at a personal level. I've made a deep dive into just my own CO2 output. The facets of my life that turn loose CO2 (and other climate-forcing gasses) are myriad.
Having said that, I think that as a 'job' 'climate jobs' are more like an ethic, than a goal-directed job. I'll simply call it 'climate consciousness'. As such, 'climate consciousness' falls into a subcategory of what engineers tend to do automatically:
1. Design-in efficiency;
2. Reduce weight and unnecessary expense;
3. Get the same thing done, with less resources.
An overly-robust approach to these things is to diminish and resources, as well as features and capabilities to things that already exist. In other words, if the climate approach is to live an austere Greta-Thunberg existence of sailing port-to-port over 7 days, what otherwise would occur by jet in 7 hours, then those jobs aren't just going to be invisible, but likely non-existent (notice how many rickshaw drivers there are lately?).
Still, I think there is room for work in the educational phase of 'climate change' -- namely, expressing, daily, given your home, transport, nutritional, etc. needs, what you changed, each day, to get stuff done, with less carbon, etc. outputs.
I'm currently working on an app that does one simple thing. Informs electric vehicle drivers how to grab some of the grid, when renewables are dominant -- and quantify that in terms of CO2 g/kWh. Many people don't know, that charging an electric car in Texas, at the right times, gets the driver access to CO2 g/kWh approaching 245 g/kWh (a typical California daily average (1)). My app shows how to amplify the tools of EVs and renewables.
Having said that, here is a short laundry list of jobs that are more climate-aligned than your average job:
* Contract transactions with land-owners for solar and/or wind leases;
* Power Purchase Agreement transactions and legal review;
* Landfill environmental clearance and design;
* Airborne drone delivery of urgent items (pharmaceuticals; factory parts; exotic tools; medical consumables);
* Fusion reactor research.
I'll leave it to others to add their favorite job category.
1. https://www.caiso.com/todaysoutlook/Pages/emissions.html