Didn't King Fred want to know why Herringbone 'Retired'?

The chief advisor's retirement is announced to the king with indirect speech, so we cannot rule out that king Fred did indeed question why, but Spittleworth smooth-talked his way out of it:

When King Fred woke next morning and was informed that his Chief Advisor had retired at this critical moment in the country’s history, he was furious. It came as a great relief to know that Lord Spittleworth would be taking over, because Fred knew that Spittleworth understood the grave danger facing the kingdom.

The Ickabog, Chapter 20 - Medals for Beamish and Buttons

Other than that, consider that Fred is a rather foolish king, and seems to eat out of Spittleworth's hand. The fact that someone he thinks he can trust, was there at the time of the ickabog's attack, and "[understands] the grave danger facing the kingdom" seems to alleviate his immediate concerns for the chief advisor. (He had more pressing issues, like keeping peace and breakfast).

---

Chapter 22 has recently been released, which addresses this question from the perspective of the other advisors:

But what, you might ask, of the eleven other advisors, who’d worked under Herringbone? Didn’t they think it odd that the Chief Advisor had resigned in the middle of the night, and never been seen again? Didn’t they ask questions, when they woke up to find Spittleworth in Herringbone’s place? And, most importantly of all: did they believe in the Ickabog?

Well, those are excellent questions, and I’ll answer them now.

They certainly muttered among themselves that Spittleworth shouldn’t have been allowed to take over, without a proper vote. One or two of them even considered complaining to the king. However, they decided not to act, for the simple reason that they were scared.

The Ickabog, Chapter 22 - The House with No Flags

So it seems like his failure to question where the Chief Advisor went could be attributed to Fred's suggestibility and naïvety.