There are mentions in Rebels of "the Empire came/will come", which suggests that there are many ex republic systems that were not directly under the Empire's control.

What happened? These were neutral systems the Empire tries to pillage, or perhaps ex Separatist systems? Or perhaps non-Republic systems that the Empire has decided to conquer all the way?

Is the Rebellion the only military opposition the Empire is facing? Are there external threats the Empire has to dedicate their forces toward? Or perhaps just weak, unaligned systems ripe for easy conquest?

They have a long 'to do list' I'm sure.

There are plenty of planets out there with neutrality, some that may have opted to leave the republic.

The other issue is despite Palpatines flawless plan to bring the republic under heel, having him rule over them in name and deed are two separate issues and the issue of consolidating power is the war currently been fought.. There are plenty of systems under the empires rule that try to thrive as they did in the republic before which is precisely what the empire is looking to stamp out; the removal of a planet's core identity with the vision of the empire. Plus there's plenty of regions in this universe left to take over, including Hutt and Wild Space.

If the Empire doesn't need anything on the planet, the planet doesn't have a large enough population to support a military to threaten a Star Destroyer or they're way off the beaten path and keep to themselves, then the Empire's going to ignore them -- for a while.

Eventually they'll get around to subjugating them, but it's not something that they're focusing on right now. At the moment, they're working on the Rebellion and assorted Super Weapons.

Check the specific timeline of the clone wars and the consolidation of the empire into the civil war. Most of the conquest went in the Outer Rim Sieges, and probably still continued politically as the governments replaced by moffs.

There are mentions in Rebels of "the Empire came/will come", which suggests that there are many ex republic systems that were not directly under the Empire's control.

What happened? These were neutral systems the Empire tries to pillage, or perhaps ex Separatist systems? Or perhaps non-Republic systems that the Empire has decided to conquer all the way?

Is the Rebellion the only military opposition the Empire is facing? Are there external threats the Empire has to dedicate their forces toward? Or perhaps just weak, unaligned systems ripe for easy conquest?

Depends how you define 'conquest'. In terms of external powers/states, there are a few, but its probably telling that the biggest and most powerful of those is the Hutts, who are playing very carefully lest the Empire drop the gloves and wipe them out. The main reason the Empire doesn't is it would be expensive as hell. Far more profitable to have the Hutts keep paying them off in taxes/tribute.That seems to be the general rule of thumb for independent groups, assuming some Moff doesn't get it through his head to go conquer a place 'for the glory of the Empire'.

As for basically everything else, this is where the term 'conquest' gets tricky, because the Empire at least nominally controls most of the known galaxy, and most of the known galaxy recognizes that authority. Even the Hutts pay lip service to that ideal. The Rebellion is, obviously, the exception to that rule of thumb. So it less the Empire popping up above a neutral/hostile world and going 'you are now part of the Empire, kneel before the throne' (though they do that as well) and more the Empire showing up and going 'as part of Empire, you are obligated to supply X. Failure to supply X will result in penalties up to and including Base Delta Zero initiatives.' Depending how diplomatic the Imperial is being, they may just leave the last bit implied. And if they are refused, well that's where military force come in.

I think their model is: send a SD or two and hammer the local population in line, then set up a regional governor that reports to the sector Moff to maintain control.

Which is why you have sector fleets available to Moffs who can send Imperial resources to a planet/system under his purview if there is any unrest.

I imagine the Empire also has discretionary forces that are able to respond to threats galaxy wide. Until the full on Rebellion comes along, then those discretionary forces are spent looking for and engaging the rebels.

I don't think the Empire was just a blunt hammer approach. Palpatine was a pretty crafty dude. I'm sure a lot of the systems were 'controlled' using his dastardly corruptive dark Force powers on the right leaders coupled with good ol bribery and coercion.

I'm sure there was a bit of WW2 island hopping strategy as well. Cutting systems off, interdicting shipments to them, holding critical infrastructure at risk and forcing compliance, etc.

I suspect that the Empire's approach to worlds that held no particular strategical or logistical importance was something along the line of, "pay your taxes, don't harbour dissidents and don't make waves and we'll leave you alone to govern yourselves; cause trouble and we'll swing by and make an example of you".