The application for a property called Cwm Gwalley was been made by Cllr E Michael Jones.
The plans were to provide additional living space to the existing house and a front porch.
Originally, the building had been a barn and used for agricultural purposes.
Until November 2020, Cllr Jones was vice-chairman of the planning committee.
Rules mean that applications made by councillors, county council staff and close members of their family are brought in front of the planning committee for a decision.
Cllr Jones was not at the planning committee meeting on Thursday, April 29, when the application was discussed.
Following a presentation on the plans, Councillor Jon Williams asked for confirmation that there are no listed buildings close to the property?
He was told by planning officer Charlotte Ford that there were no listed buildings closer than 500 metres to Cwm Gwalley.
Councillor Gwilym Williams said: “The community council is in favour, the bat report is fine, this is a minor extension to an existing house.
“I don’t see any objections and it’s only come to us because he’s a county councillor, normally it would be delegated.”
Cllr Williams proposed recommending approval.
The proposal was seconded by committee vice-chairman Cllr Gareth Jones who said: “It looks a very straight forward application, enhancing an existing property.”
Planning committee solicitor, Colin Edwards added: “I can confirm that I have reviewed the papers and the application was processed normally in accordance with the protocol.”
The application was approved unanimously.