Oh when it comes to the Spore Drive, absolutely. But anytime that major engineering problems crop up he’s still usually the one asked to deal with it somehow. Yet we know that there’s a chief engineer on board. Reno has a line in season 2 where she comes in saying that ‘The Chief’ sent her to check something out. That’s also where he line comes from about how she doesn’t know why that lab is considered propulsion. Also the ‘pick mushrooms off my pizza’ bits. I may have seen Discovery too much recently.

So we’ve got Commander Jett Reno in Engineering who works under a CEO. We’ve at least met the CMO on Discovery. She doesn’t get a whole lot of screentime but she exists. I really wanna know who the engineer was on Discovery throughout all the shit of the last 4 seasons and I really want that Engineer to show up on the Bridge in Season 5 just bitching. Having a whole monologue about how they’ve had to deal with tons of shit from the past and how no one has checked in on them. Burnham then with a look on her face like “Fuck. Shit. Fuck shit fuck.” Saru standing in the corner equally as embarrassed.

Edit: Thinking about it… Chief Engineer is the only Chief we’ve know nothing about.

Chief Medical Officer - Tracy Pollard not Hugh Culber. Memory Alpha is inaccurate on this front. Not sure why but they’ve labeled her as head nurse and Hugh as CMO. In Season 1 she’s the one giving orders to Hugh and everyone else. I’m also 90% sure there’s a line about Hugh saying she’s his boss. In Season 2 she’s also the one to allow Saru and Culber to return to active duty. Culber was also going to transfer to Enterprise, and was allowed, at the end of Discovery Season 2. No chance in hell that the CMO is just going to bounce around with no problem.

Chief Science Officer - Numerous. We’ve seen a few people hold this role over the show. Both Saru and Burnham have held this role throughout the show. I think Tilly may have as well during Season 4 before going to Starfleet Academy but I’m not entirely sure on that front.

Chief Security Officer - Numerous. Started with Landry before being handed over to Tyler. Season 2 didn’t really have an obvious one around but Na’an stepped in to fill the role over all until she departed. At the moment we don’t know who fills that role. Maybe Rhys considering he’s the tactical officer but who knows.

Chief Engineering Officer - We have only ever seen two references to a Chief Engineer on Discovery and one was a joke. There’s the one I mentioned before with Reno but there’s also a joke in Season 1. When they first land in the Mirror Universe, Lorca is about to answer the hail before Burnham stops him saying that he’s not the captain. Tilly takes over and hands it over to her ‘chief Engineer’. Lorca then starts speaking with a fake Scottish accent.