I have already received and signed an offer letter for a position as an assistant professor. This position will start next fall, to give me time to finish my post-doc. I'll be applying for a number of grants over the next year. Should I include my future position on my CV for these applications? It seems like relevant context for reviewers to have, but I've never seen anyone do it.
Typically grants are administered by institutions, and therefore the grant is really to the university and not the individual. Therefore, it is likely that you will be applying for funds on behalf of your new, rather than current, affiliation.
In that case, it certainly makes sense and is more or less necessary to include that new institution.
For individuals who are not currently located at the applicant organization, include the expected position at the applicant organization and the expected start date.
referring to the "biosketch" document which for NIH grants serves the purpose of a formatted CV. And also:
If your proposed career development award will be at a different site than your current institution, the proposed sponsoring institution will be the applicant organization. You must affiliate your Commons account with that institution so that you have access to records submitted on your behalf.
(this is referring to the class of NIH grants that would most likely be applied for by someone transitioning from a post doc to asst. professor position)
I would suggest looking for similar instructions for whatever organizations you are applying for funding from. You also likely should be working with grant support people at your new institution.