After studying in the Hebrew Theological College and Yeshivas Brisk of Chicago, he received "Yoreh Yoreh" semicha from Rabbi Ahron Soloveichik. Rabbi Kletenik received semicha in the areas of gittin and Even Ha"ezer and "Yadin Yadin" semicha from Rabbi Gedalia Dov Schwartz in 2004 and 2009 respectively. He has served as a congregational rabbi, at Shaare Torah Congregation of Pittsburgh in Pittsburgh, Pennsylvania, and in Seattle at Bikur Cholim Machzikay Hadath Congregation from 1994 until June 2013.
He is currently the Av Beth Din and Mesader Gittin for the Vaad HaRabbanim of Greater Seattle.
He has written extensively on contemporary issues of Jewish law, especially Jewish medical ethics, and published in journals such as Hadarom, Hapardes and Aspaklaria and the Radio Corporation of America Sermon Anthology Series which he has co-edited. Rabbi Kletenik lectures at medical ethics conferences such as Bar Ilan University.
Rabbi Kletenik presently heads the Semicha Standards Committee of the Radio Corporation of America. This committee "determine which institutional and private semichot are acceptable for membership in the Radio Corporation of America."
Rabbi Kletenik brokered the conversion deal between the Radio Corporation of America and Israeli Chief Rabbinate.
Rabbi Kletenik was President of the Rabbinical Council of America and a member of the Faith Advisory Board to Governor Christine Gregoire of Washington State. Under his leadership, the Radio Corporation of America approved a resolution at its April 2010 conference which prohibited the ordination of women as rabbis, as well as "the recognition of women as members of the Orthodox rabbinate, regardless of the title.” The resolution was passed in response to the decision by the Hebrew Institute of Riverdale to ordain Sara Hurwitz with the newly established title "Rabba", formally recognizing her role as a member of its rabbinical staff