No one "somehow dies" in Dungeon World.
Yes, philosophically, all adventurers are mortal, each adventurer's death is an accident, nobody wakes up in the morning thinking "well, I guess this is the day the Apocalypse Dragon dissolves me into chaos". However, mechanically, nobody takes damage unless you the GM decide they do. (Okay, some player moves like Penitent involve self-initiated-harm, but you the GM are also deciding whether or not to allow them, so.)
Dungeon World is not a game that works well if you decide not to interest yourself about the player characters and their abilities and their hit points and armor, so you, the GM, should always know how much armor and how many hit points each of your players have at all times. This isn't super challenging - armor is a single digit and hit points are low doubles at best. So you know, when you're thinking about dealing damage, whether or not that damage is going to kill somebody.
You should be a fan of the characters, right? Give them what they've earned, don't take away what makes them interesting? If this is an interesting time to die, if it's a finale they've earned, sure, go ahead. Otherwise, when it comes time to make a GM move, you have "deal damage" and at least a dozen other options. Pick one that makes sense. If "nothing else makes sense", that's a sign that you might have incautiously set up a scene and ad-libbed some opposition in there without a clear idea of what they wanted there so you're defaulting to murder. But that's a terrible default. Take some time out to think.
But when a PC gets an interesting death, that's in the process of trying to resolve something important, right? And the thing about resolving something important is that there's time afterward to reflect on less important things. Like: Warlord Krozar is dead, the orc armies are in full retreat... what are we to do with Fightgar's broken body?
Be a fan of the replacement, too.
So from the question it sounds like you might have this idea that Fightgar dives to protect Clericsdottir, takes Warlord Krozar's axe to his entire ribcage, remains conscious just long enough to see she's safe -- and then, in an instant, the spark of protagonism jumps over to Regdar the hired bodyguard, who has suddenly obtained a signature weapon and a desire to bend lift some gate bars.
But that's not really fair to anybody, is it? You're not going to just demand everybody break this fight, so Steve, player of Fightgar, can make a new character. Part of what made Fightgar interesting can be summed up as he will be missed. Let him be missed! At least for a little bit. Besides, maybe Steve has a hankering for one of the other options:
Maybe a hireling becomes a full-fledged adventurer worthy of a whole share and a part in the real action. Maybe the characters in the party find a new friend in a steading, willing to join them. Maybe your character had a vengeful family member who now seeks to take up their blades and spells to make right what happened. In any case, make your new character as you normally would at level 1.
-- "After Death", from the repo's Playing the Game section
but neither of those other options could be fifteen feet away from Warlord Krozar and closing fast. Please don't pressure Steve to take up a character he doesn't want just for the sake of making the next ten minutes a little more interesting to him.
If Steve wants to take up Regdar, then you can pick up with Regdar at the same time you'd pick up with Bightgar, brother to Fightgar, arrived from afar on a mission of vengeance, or perhaps with John the Gold, guard captain and friend to the party who had to organize the last line of defense against Warlord Krozar. You'd have the whole aftermath of that interesting event to give Steve's new character a proper introduction, explain the bonds, maybe let Regdar pick up a proper Fighter's set of starting equipment if that's the way it broke.
You have enough time to give this brand new character what they've earned: a proper introduction as its own focus, not saying how-do-you-dos with Warlord Krozar still waving his bloody axe around screaming for covering fire.