Here is the full story from page 14 of McGilchrist:
There is a story in Nietzsche that goes something like this. There was once a wise spiritual master, who was the ruler of a small but prosperous domain, and who was known for his selfless devotion to his people. As his people flourished and grew in number, the bounds of this small domain spread; and with it the need to trust implicitly the emissaries he sent to ensure the safety of its ever more distant parts. It was not just that it was impossible for him personally to order all that needed to be dealt with: as he wisely saw, he needed to keep his distance from, and remain ignorant of, such concerns. And so he nurtured and trained carefully his emissaries, in order that they could be trusted. Eventually, however, his cleverest and most ambitious vizier, the one he most trusted to do his work, began to see himself as the master, and used his position to advance his own wealth and influence. He saw his master’s temperance and forbearance as weakness, not wisdom, and on his missions on the master’s behalf, adopted his mantle as his own – the emissary became contemptuous of his master. And so it came about that the master was usurped, the people were duped, the domain became a tyranny; and eventually it collapsed in ruins.
Based on my reading of Nietzsche's corpus, I can say with a high degree of confidence that (a) this story appears in none of Nietzsche's published works from The Birth of Tragedy onwards, and (b) it is inconceivable that the Nietzsche who created those works could have written such a story. For example:
Wise spiritual master ... and who was known for his selfless devotion to his people
-- Nietzsche abhorred selfless devotion and herds.
As his people flourished and grew in number, the bounds of this small domain spread ...
-- Nietzsche advocated passionately for the flourishing of exceptional human beings, not the flourishing of seemingly ordinary peoples such as these.
... and with it the need to trust implicitly the emissaries he sent to ensure the safety of its ever more distant parts
-- Nietzsche couldn't have cared less about either the expansion of the small domain or the safety of its more distant parts. He would have attached zero value to both expansion and safety. I also doubt he would have trusted emissaries.
... It was not just that it was impossible for him personally to order all that needed to be dealt with: as he wisely saw, he needed to keep his distance from, and remain ignorant of, such concerns
-- Nietzsche wouldn't have cared about ordering all that needed to be dealt with. In the remote event he would have cared, he would not have wanted to remain willfully ignorant of such concerns -- willful ignorance of matters important to him not being a value to which he would have attached any esteem.
I could continue, but it's already abundantly clear Nietzsche could not have written such a story.