WASHINGTON—Transportation Secretary Elaine Chao has retained shares in a construction-materials company more than a year after the date she promised to relinquish them, federal disclosure forms show.

Shares of the company, Vulcan Materials Co., the country’s largest supplier of the crushed stone, sand and gravel used in road-paving and building, have risen nearly 13% since April 2018, the month in which Ms. Chao said she would be cashed out of the stock, netting her a more than $40,000 gain, corporate and government filings...