Cllr Simpson’s announcement comes a year after he survived a no confidence vote by the opposition Independent Group on the council.
The unaffiliated councillor is believed to be the only council leader not part of a political party or council group.
He has led the council for seven years.
Cllr Simpson has said that while he is standing down as leader, he intends on continuing as Lampeter Velfrey’s county councillor.
Cllr Simpson said: “I will not be standing at the next AGM in May. It has been seven years, and it is time for someone else to take the helm.
“It is a very demanding position, one that I have enjoyed, but it does not give me any time for my wife, children and the grandchildren.
“It is time to stand aside and let someone else do the job. I have had the privilege of working with some outstanding cabinet members, officers and colleagues in the chamber.”
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