Broom was not a distinguished patriot. His only recorded service was the preparation of maps for George Washington before the Battle of Brandywine, PA. In 1776, at 24 years of age, Broom became assistant burgess of Wilmington. Over the next several decades, he held that office six times and that of chief burgess four times, as well as those of borough assessor, president of the city "street regulators," and justice of the peace for New Castle County.

Broom sat in the state legislature in the years 1784-86 and 1788, during which time he was chosen as a delegate to the Annapolis Convention, but he did not attend. At the Constitutional Convention, he never missed a session and spoke on several occasions, but his role was only a minor one.

After the convention, Broom returned to Wilmington, where in 1795 he erected a home near the Brandywine River on the outskirts of the city. He was its first postmaster (1790-92) and continued to hold various local offices and to participate in a variety of economic endeavors. For many years, he chaired the board of directors of Wilmington's Delaware Bank. He also operated a cotton mill, as well as a machine shop that produced and repaired mill machinery. He was involved, too, in an unsuccessful scheme to mine bog iron ore. A further interest was internal improvements: toll roads, canals, and bridges.

Broom also found time for philanthropic and religious activities. He served on the board of trustees of the College of Wilmington and as a lay leader at Old Swedes Church. He died at the age of 58 in 1810 while in Philadelphia on business and was buried there at Christ Church Burial Ground.