Prior to becoming a general authority, Parmley had served as the chief of cardiology at the University of California, San Francisco and did studies primarily relating to cardiovascular pharmacology.

From 1957 to 1958 he served as an LDS missionary in the Northwestern States Mission based in Portland, Oregon.

[6] Parmley also co-authored with Stanton Glantz several papers on the health effects of passive smoking that were covered by the news media.

Prior to his call as a general authority, Parmley served previously in the church as a bishop, stake president, and area seventy.

As a general authority, Parmley served in the presidency of the church's Africa Southeast Area.