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Well, I'd recommend trying not to just ignore that the old die doesn't fit; ideally, you'd imagine a way to bring it into relevance, because it's the combination of the randomized elements that give your Dungeon Hero stories their depth and replayability.

But if you're drawing a blank for a particular pairing, it's perfectly fine to just imagine the newer die as "doubly relevant" in that situation; there's no problem doing that if you want to keep the tempo up and it's taking too much time to think up something interesting.

Below are some strategies for finding a way to make those pesky dice relevant. Hopefully, some of these will help spark ideas as to how you can solve this problem when you encounter it.

Let's imagine you generate two trait dice while trying to sneak into an old, run-down castle.  The older die is d8 Shadowy gatehouse and the newer die is d10 Climbing the stairs of the castle. These two dice describe two geographically distinct traits, so it makes sense that you might want to tweak the meaning or have a hard time connecting them because how can the adventurer be in both places at once?

In this situation, you could:

• Tweak the old environment trait to extend it to the current situation.  Here, you are just adding to or expanding the original trait to give it more "reach".  "As I was leaving, a gatehouse guard came back from patrol, found his fallen comrades, and is now following behind me and waiting for a time to strike. I notice him following me as I'm climbing the stairs of the castle."
• Interpret the situation as the transition between those two traits.  Maybe neither trait is what's affecting the adventurer right now, and it's the liminal space between them that the adventurer finds challenging.  "I need to make my way from the gatehouse to the castle entrance, but it means crossing the courtyard without being seen..."
  
• Imagine a "twist" that happened back in the context of the first die that is only now coming to light. "It was then that I realized my wineskin had been slashed open, and everywhere I'd walked had been trailing a dribble of bright red wine. And here I was, walking right up the main staircase of the castle..."
• Imagine a lingering effect of the last situation that you rolled.  Say the last situation you rolled was a fight with two guards. You might imagine a lingering effect of the fight like so: "The fight in the gatehouse had winded me. I climb the stairs, trying to keep my breath silent as I labor to ascend them."
• Shift to a nearby trait descriptor. If the first die doesn't make sense any more, you can always replace it with a descriptor you skipped over but didn't use. Try grabbing the descriptor of an unused trait immediately before or after the original die (or before or after the new die). For example, if the environment trait after d8 Shadowy gatehouse is d10 Alert guards on patrol, you could switch to that die's descriptor.  This will keep the meaning of the dice in the same general context of the story without you having to invent anything. I'd recommend keeping the die size of your original die, however.
  
• Invent something totally new to replace a die, as long as it's interesting and relevant to the situation. "Just as I was about to ascend the stairs, a cluster of giggling handmaidens came bustling down the corridor, forcing me to duck into the shadows under the stairs to avoid them seeing me."

Hope this helps!