It's not "leftist" necessarily, but all leftists should inform themselves about the Russian Revolution IMO, which is covered by season 10 (the final and currently ongoing season) of the Revolutions|^Spotify^ podcast.

Mike Duncan isn't explicitly leftist or anything, but he really does his homework and portrays things in a really neutral way. Whether or not you are a big stan of the USSR and what came after, the Russian Revolution was the most successful attempt at overthrowing capitalism (to an extent), and any future movement should learn from and analyze all aspects of what happened in those years.

Citations Needed|^Spotify^ is my other favorite with their in-depth media criticism (if you like Chomsky's stuff, you'll probably like what they have to say).

Behind the Bastards

I think Cool People who did Cool Stuff is pretty leftist/anarchist.

Not necessarily political in content, but clearly lefty:

• The Dollop/The Past Times
• Behind The Bastards

Adding:

• 'Tech won't save us' (Leftist/Marxist critical Analysis of Techtrends)

• 'Trashfuture' (About the absurdity of Start-up Culture and UK Politics)

Chapo Trap House

None of these are really my cup of tea but any love for Last Podcast on the Left? That counts right?

"Well there's your problem", about engineering disasters - it's also a YouTube channel but there are podcast feeds and it works as audio (that's how I listen). Also "Know your enemy" is a leftist look at the right.

Working class history

Popular front even tho it isnt what i would call lefty but it does cover interesting conflict/protest stuff

Go visit maximum fun, the whole network is usually centre left or leftist. Whole range of topics and types with that perspective.

99 PI comes to mind as well Or wait wait don’t tell me’s podcast

Reasons to be Cheerful isn't necessarily a 'leftist' podcast (One of the hosts is the former leader of the Labour party in Ed Milliband), but the show spends a lot of time talking about leftist ideas to improve the world.