A pompous person; a stiff, self-important bore (1913+)
The Dictionary of American Slang, Fourth Edition by Barbara Ann Kipfer, PhD. and Robert L. Chapman, Ph.D. Copyright (C) 2007 by HarperCollins Publishers. Cite This Source
Idioms and Phrases with stuffed-shirt
An overly formal or pompous person, as in She's such a stuffed shirt that I'm surprised you'd invite her to a barbecue. This expression alludes to a shirt filled with paper (instead of a real person).
[ c. 1900