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The players have done their original purchasing. As a rule of thumb, setting the stopwatch going on our phone at the start of buying, we can count every 20 minutes that's passed as one day. This includes the time the players spend skylarking while looking over the equipment lists, as this is what people do when they shop. They stop, they rest, they enjoy themselves. The time takes into account the players searching through several stores, crossing and recrossing the town or city, making inquiries, haggling — another subject for another day — and so on. Each "day" is food that's eaten, lodgings that must be paid for, and the time of warm weather drifting away towards autumn, or the rainy season.
Eventually, one character draws out the ring found in the kobald lair and asks, can I sell this? It's a dark red carnelian stone in a white gold setting, with a vaguely familiar cross-hatched pattern on it. Two lines perpendicular to two lines, surrounded by a circle. When described, the player remarked, "Where did we see that before?"
"Yes, of course," we say, directing him to a jeweler's shop. In a few moments, we know as dungeon masters that the jeweler is going to see the ring, recognise it for what it is — a ring owned by the present-day noble's lost father. And then ... what?
These are difficult moments to run. The easiest answer is that the jeweler informs the noble, who seizes the players, demands to know how they got the ring, then offers them a huge reward if they return to the dungeon and find the bones of the noble's father. It works as an explanation, but we might be confused into thinking that because something works, it's a good proposal. That's often a mis-step in resolving connections like this in the game.
First, because this particular explanation reduces the drama to a trite exchange of one kind of good for another: money for bones. As a motivator, it isn't meaningful. As discussed with the last post, the player characters are going to accumulate money anyway, no matter where they go or what they do. Just as cost isn't much of an obstacle, it isn't much of a stimulus, either.
Second, the presence of the noble, who has so much more power than the players, produces an imbalanced relationship, one that leverages the players against their will. If they don't fetch the bones, then obviously the noble won't be happy. Even if we know in our DM hearts that the noble won't hold it against the party, we can't legitimately say that to the party without breaking the fourth wall — and the party would have no reason to believe us anyway. When providing a reason for the party to do something, be careful of situations where they're acting in a powerful NPC's stead: try not to hinge the connection on something the noble would view as highly personal — such as a lost father.
Third, going back to the dungeon is something the players were going to do anyway. The ring's back story needs to add dimension to the narrative thus far; that is, something greater than just the loss of a father by a son, which is rather one-dimensional in scope. We need to know more. The ring is incidental. Anyone of importance and power might happen to be wearing a ring when they die in a dungeon. The larger questions that need answering are about the father himself: who was he, what was he searching for, what were the facets and consequences of his life, and his decision to plunge into this dungeon? We might produce details to suggest that the father's death was inevitable; that it came about because the father courted death foolishly; it may even be that the father was so awful, that the region was grateful for his death.
But empathy is only a second dimension in our story; the element we want to add to make the players feel something more about this ring than that it happened to be on a dead man's finger. The third dimension revolves around an as-yet unseen conflict that potentially arises from this minor discovery. Normally, when we imagine the death of a person, we see the end of something; but this is Dungeons and Dragons. There be magic in this realm. What forces have been put into play by the disappearance of the princess into this dungeon; and what forces are stirred by the death of the noble's father? And now, with the players entering the dungeon, what consequences are yet to reveal themselves?
Much of this depends on what's in the dungeon. And in the answers to these questions being asked. But let's say, as an opening gambit, that when the living noble confronts the party about his father, he begins by urging the players NOT to return to the dungeon — for their sake. What if that's followed by a story of things that awaken the players' doubts? "My father was not a good man," says the noble to the party. "He ... did things he shouldn't have done. When he set out that day, I was but 17 ... and I was told that his choice to venture forth was to make restitution against demons that my father awakened."
The noble pauses before going on. "I don't know what that means," he says. "And I've not met a soul who can explain it to me. But though my father did not return, it's also a fact that nothing has been heard of any of this in 25 years. Perhaps it's best if we presume my father achieved his quest — and paid with his life in the bargain. Leave it alone, dear friends. Leave it be as a favour to me."
This opens all kinds of doors. The players can hear the word "demon" and rightly decide, "Um, we're out." Or they might assume that as DM, we're not going to get them into something deeper than they can handle ... and in any case, players HATE being told not to do things, even when the advice is there to save their lives. So they say to the noble, "Good sir, your heart is in crisis. Let us go to the dungeon and put your heart to rest."
And so on. We haven't returned to the dungeon and yet, here, there's conflict. Should we go, or not? Is going a good idea, or a bad one? If we fail, what will the noble do? If we succeed, surely he'll be grateful. But he hasn't promised anything. Should we go on our own volition, without this noble's urging?
This is a thousand times more intense than exchanging bones for money. When the players aren't playing the game, when they're at work, when they're showering, when they're digging in the garden, they're thinking about the choices they've made. It's D&D in the players' heads, all the time. Not just during the session.
I can't give a blueprint on how to produce a 2nd and a 3rd dimension to your game narrative, but I can reiterate some of the points made above.
Avoid "simple" explanations. Avoid exchange-based motivations. Don't reward players for doing something they're already going to do. Give details about each NPC's motivations and memories, from their point of view, as though the noble or the noble's father were player characters that you, as DM, ran once, or are running. Consider reasons why players ought NOT to do something, as well as why they should do it, and then lay out both sides in your exposition/backstory. Put the players in a position where the right answer isn't plain. Make them decide what's the right thing to do.
If we spend too much time thinking that it's our role to push the characters to act, we forget that there's conflict in pushing the characters NOT to act. If they feel the game world is fluid, and that they have agency, then we can be quite sure they're going to do something. It's not our job to get behind them and push.
It's our job to put a fork in every road they travel.