The word contemporary is commonly used as a synonym for modern—definition 2b in Merriam-Webster—the sense being that something is contemporary with us, readers today. An example is seen in Herbert R. Coursen’s discussion of modern-day Shakespeare adaptations: “contemporary Shakespeare in any format,” he contends, “makes the script ‘relevant’ but only by ignoring much of what the original contains (xxi). Contemporary also means, more literally, “at the time of” something in the past, per definition 1 in Merriam-Webster. An example would be the statement that Shakespeare was a contemporary of Ben Jonson. Context usually makes it clear which meaning is intended, as Theodore Bernstein and Claire Kehrwald Cook both observe. But it’s not that rare, unfortunately, that the word can be read either way. (It can also happen that a writer will carelessly, inelegantly, use definition 1 in one sentence and definition 2b in another nearby.)
In your writing, do be mindful of the possibility of the past-present ambiguity of contemporary.
Bernstein, Theodore M. The Careful Writer: A Modern Guide to English Usage. Atheneum, 1985.
“Contemporary, Adj.” Merriam-Webster, www.merriam-Webster.com/dictionary/contemporary.
Cook, Claire Kehrwald. Line by Line: How to Improve Your Own Writing. Houghton Mifflin, 1985.
Coursen, Herbert R. Contemporary Shakespeare Production. Peter Lang Publishing, 2010.