I accepted a new job at my company in a different department and have a new group and manager. This group does research on a different topic than my old role and I have a sort of technical communications role in the group now.
I accepted due to the fact that it was full time, much higher pay rate, and also fit my background well which is sort of a mix of technical roles, but also communications. My last role was as a field work tech which I valued because it taught me a lot of new skills, but it wasn't a very stable job with limited hours and also uncertainty of funds for future work.
I would like to continue assisting with field work occasionally (2/3 days a month) with my old supervisor since I find it to be very educational compared to my current position. Those days would be paid for by my old supervisor and I would not log hours with my new one. I am a little concerned about bringing it up with my new supervisor since I don’t want to make it seem like I am unhappy in my role and think it may be awkward asking to not “come in” to work so I can go work for someone else. What is the best way to ask my supervisor to do this? Or would it be inappropriate to ask in the first place?