Kimberly Guilfoyle has faced allegations that she engaged in sexual misconduct when she worked as a host at Fox News, leaving the network to pay out a multimillion-dollar settlement to avoid trial.

It was an announcement made amid a swirl of tabloid speculation: Kimberly Guilfoyle, a loyalist of President-elect Donald J. Trump and — more pointedly — the fiancée of his son Donald Jr., had been named as his choice to be ambassador to Greece.