To bring up to date; often specifically to set a historical narrative in a modern context
1948, Gordon Allport & Leo Postman, The Psychology of Rumor, page 91:
In the few instances where the initial description is couched in the past tense, immediate reversal occurs and the scene is contemporized by the listener.
(marketing) To modify, repackage, or present a well-known or traditional product or brand in a way that appeals to contemporary consumers.
2013, Michael Moss, “The Extraordinary Science of Addictive Junk Food”, in The New York Times Magazine:
Oscar Mayer tapped him to try to find some way to reposition bologna and other troubled meats that were declining in popularity and sales...when Drane began working on the project, his orders were to “figure out how to contemporize what we’ve got.”