Clark, whose full name is Johnson Pepper Clark Bekederemo, was born on April 6, 1935, in Kiagbodo, Nigeria. He is the son of Clark Fuludu Bekederemo, an Ijaw tribal leader, and his wife, Poro. Clark attended three different primary schools in the 1940s for his elementary education. He then went to a government college in Ughelli, where he earned his Cambridge School Certificate in 1954. After spending a year working as a government clerk, Clark enrolled at the University of Ibadan.

While at the university, Clark became actively involved in literary pursuits. He established The Horn, a poetry journal, and also wrote his own poetry. His first volume of poetry, Poems, was published in 1962. Clark also wrote his first play, Song of a Goat, which was produced at the university in 1961. He graduated with honors in 1960, earning his B.A.

After graduation, Clark primarily worked in media-related roles. He spent a year as an information officer for the Nigerian government. In 1961, he worked for a year writing and editing for the Daily Express newspaper in Lagos, Nigeria. His work at the newspaper led to a prestigious fellowship at Princeton University in the United States from 1963-64. Although he had negative experiences there, which he recounted in his memoir, America, Their America, his time in the U.S. was productive. During this period, Clark wrote The Masquerade and The Raft, which, along with Song of a Goat, formed a trilogy published in 1964.

Upon returning to Nigeria, Clark held several fellowships, including one at the University of Lagos. In 1966, he wrote another play, Ozidi. However, for the next two decades, he primarily focused on writing poetry and nonfiction scholarly work related to his job. Clark joined the University of Lagos as a professor in 1966 and was promoted to chair of the English Department in 1970. He retired in the early 1980s.

After leaving teaching, Clark returned to the theater. Together with his actress wife, Ebun, with whom he had three children, he founded the PEC Repertory Theatre in Lagos in 1982. In addition to running the theater, Clark continued to write plays, including another trilogy about the history of the Niger Delta called The Bikoroa Plays, and poetry, including the 1985 work "State of the Union." Though Clark ultimately received more critical acclaim for his poetry than his plays, he continued to work in both fields for many years, dividing his time between his hometown and Lagos.