One thing which is clear, Jamie is technically dead when his ghost travels to the future and Gabaldon has confirmed the Highlander will be roughly 25-year-old when this happens.
The character is thought to be fighting in the Battle of Culloden around this age, suggesting he temporarily dies during the battle or at least in the aftermath.
In both the novel Voyager and Outlander season three, Jamie is at death’s door and it’s only by some miracle he’s saved.
Therefore, this would suggest Jamie will die before Claire but at this point in the story his death is only temporary and he returns to his body.
source: express.co.uk