You can have a "climate career" doing pretty much any job you would like.

You can be an IT, a dev, a mechanical engineer, an accountant in a startup working on carbon removal [1], you can be a chemist researching new ways of producing cement with less CO2 impact [2], a farmer specializing in multistrata agroforestry [3], a technician installing solar panels etc.

[1]: https://carbonengineering.com/careers/

[2]: https://drawdown.org/solutions/alternative-cement

[3]: https://drawdown.org/solutions/multistrata-agroforestry