"Political" is a pretty broad term. You want news, analysis, gossip? The
"Current Events" section of the OP is a good place to start.
Broadly, I'd recommend
Slate's Political Gabfest;
On The Media; maybe
Vox's The Weeds (I only just added that one, not sure yet if I like it or not);
The Axe Files is a really good interview show usually with political operators but often with politicians, too;
FiveThirtyEight Elections is good (gets into political reporting in addition to just the polling/modeling talk) but it's probably ending in a few weeks;
Keepin' It 1600 on The Ringer's network is an unabashedly Democrat pod (run by former Obama staffers) that can get a little inside the beltway / gossipy but the hosts are good;
Slate's Whistlestop is maybe my favorite pod right now, but that's political / campaign history.
Pretty much all of those are left-leaning or at least strongly anti-Trump. But it should give you a start. Personally I get most of my right-leaning media in text form but I'd love to see some worthy right-inflected podcasts recommended here if anybody has any?
Also shout out to poor Jacob Weisberg who I guess is on the hook to produce several hundred more episodes of the Trumpcast.