A "wry sense" refers to a subtle, dry, or slightly sarcastic understanding or perception of something. It suggests a clever and humorous way of looking at things, often with a touch of irony. Full definition
He has a very wry sense of humor, and people don't understand it right away. (businessinsider.com)
Nathan is a warm young man with a love of writing and wry sense of humor. (openadopt.org)
He's constantly expanding his knowledge of business strategy and leadership (his office contains a thick stack of books he's reading), and he's got a wry sense of humour. (canadianbusiness.com)