Premiere pro export - Colors are not right - dull/flat look

You need to set the entire selection of color management controls to what you need to work with.

That means for most users, the Display Color Management option is "on" ... unless you are working on a highly calibrated (broadcast quality calibration!) system, which most aren't.

For Mac users, typically Extended Dynamic range should also be 'on'.

Viewer gamma ... that's a pick your poison, thanks to Apple. As Apple uses a non-standard display transform for Rec.709 video on most of their machines, you can't make a file that shows the same on those machines and on most broadcast setups, TVs, and Pc/Android devices.

In fact, the Macs with Reference modes set to HDTV will fit in nicely with the rest of the world, but not with the non-reference mode Macs. An example showing that this is definitely an Apple caused thing. (HDTV setting uses the Bt.1886 display transform correctly.)

So setting viewer gamma to 1.96/QuickTime gets a look similar inside of Premiere and outside on Macs without reference modes. Though on Macs with reference modes, and all else, it will be pretty dark looking.

Gamma 2.4/broadcast is the normal pro colorist option, as all pro Rec.709 media for broadcast or streaming is produced with gamma 2.4 monitoring. Period. The output file will look lighter when displayed on Macs without reference modes ... unless viewed in VLC or Firefox browser, where it probably looks like a normal Rec.709 file.

Gamma 2.2 is an in-between sort of thing. Some like to use that ...

Next your clip, sequence, and export presets must match.

If you have auto detect log and auto tonemapping on, all HDR media will get re-spaced to Rec.709 correctly for the sequence, and then using a standard export preset you'll get what you expect. Only use presets with PQ or HLG in the preset name for sequences that are in the matching HDR format.