What is the branch of the English Parliament composed of the clergy and selected nobles?

There is no English Parliament. There has not been an English Parliament since 1st May 1707.

Answer. you are probably referring to the House of Lords which is a non elected chamber. It is not English but part of the Goverment of the United Kingdom which includes England Scotland Wales and Northern Ireland. The Queen and Parliament can elect "the Great and The Good" to the House of Lords. There are also a small number of Heritary "Lords" but this is gradually being faded away.