Podcasts like Manager Tools/Career Tools, but for academics: Do they exist? The Manager Tools and Career Tools series of podcasts are industry-oriented, but I find great value in them as I retool for an academic career. I was never a manager in my industry career, but the communication skills and practical understanding of organizations imparted are gold. 

For example, my adviser does regular 1:1s with his students and places a big emphasis on giving and receiving feedback, both MT fundamentals. Some other concepts apply less directly--for example, delegation of tasks as project leader where no one is my actual "direct report". Academic politics differ from industry politics, but fundamental principles (relationship power!) carry over.

It makes me wonder if there's some podcast series or (only slightly less desirable) Web site to help academics improve communications and ability to navigate organizational politics. I'll see what I find with obvious Google searches but I wonder if anyone out there has some favorites to recommend.
I spent a little while searching around various podcast directories for something like this, and came up blank. I suspect the main cause is that running a lab is really not that much different from running any other group of people, and the difference between PIs/advisors and managers really isn't that big. Because of that, anyone looking for podcasts on running a lab can look to any of a number of management podcasts and follow the advice there. If you're a bad advisor, you don't care anyways, so you're not looking for advice.

That said, I was surprised that I wasn't able to find any podcasts focusing on being an academic, rather than about the topic of academia itself. (I did find this one episode of this university-level teaching podcast, but that seems to have been a one-off episode.) Interestingly enough, someone recently posted a very similar question on reddit, with no good answers other than "Check out chronicle.com." I'm starting to suspect that the answer to your original question is "no".