The question is basically "who explores when there is a high likelihood of death?"
In the actual medieval period there were plenty of folks with a much more pragmatic approach to death, so simply good pay could get a number of volunteers to go through the portal, recon the other side (if they survive to get there), and report back. Establishing that pay is sent to the family for those that never report back (and presumably die on the other side) is key. Of course unless there are instructions on the portal about the consequences of connecting to a destroyed or blocked portal, I'm not sure how you would know that failure to return could mean a "dead end" gate address or just an inability to return (they can't "dial back", can't reach the return gate because it opens into a pit, are held prisoner, etc). Anyway, the quality of these pseudo-suicidal folks would probably be fairly low, but so long as their mission is just "get to the other side, turn around and come right back" they should suffice.
A sufficiently powerful king figure could compel soldiers through, but I think he would either have to conceal the fates of prior missions or demonstrate that most (like 70-80%) of gate addresses lead to a safe destination. In the pre-modern era there were travel perils aplenty, from storms to raids to just getting lost in the wilderness. So a certain level of risk was accepted, but few would go into near certain death unless there was a fundamental compulsion to do so (ie a religious "God has commanded this!!" zealous fervor) or some sort of immediate risk for NOT going (the current place is being destroyed/invaded, so without an escape route everyone is dead anyway).
Assuming most portals lead to (immediately) safe places, the usual adventuresome types would gladly explore the other side. Private ventures could fund these missions, contingent on keeping a large share of any profits. The explorers would be gathering exotic animals, plants, and the like, as well as looking for valuable mineral/precious metal deposits. A key member would be a cartographer to map the area and an astronomer (sailor?) to attempt to determine the rough location based on celestial positioning (such as it has been developed in your world). These types of folks are far to precious to risk in the initial portal test however, they would be saved for follow-up explorations.
Another option is to first send through some sort of caged or hobbled animal. This obviously won't verify that the portal is clear, but if you wait an hour or so, then send a human test subject, they could immediately verify if the animal is alive. This would confirm that the air at least is breathable, and probably determine if there are aggressive animals in the immediate vicinity. The key objective is to maximize the ability for a person to get in and get out as quickly as possible but still have the most information as possible, since determining that the gate leads to an open portal is the most critical piece of information.
Opening up a portal directly into a hostile kingdom that could retaliate would be a major concern. Perhaps the return address, if it has to be inputted at the other end, would be entrusted to just one loyal person (the others perhaps given fake address leading to known dead ends) to ensure it won't easily fall into the hands of unknown aggressors. Obviously the low quality initial test subject would have to know it (and his loyalty to the kingdom may be suspect) but that is a known risk and hopefully he will be in and out so quickly that no one could stop him. If the home gate was found in a condition that would have allowed it to be used (ie it wasn't blocked in some fashion) then it would be a reasonable assumption that NO ONE ELSE is currently using the gate system, so none of the gates probably lead directly to an inhabited area.