Complex sentence: One of the strongest supporters of the president's war policy was Peter J. Brennan, president of the Building and Construction Trades Council of Greater New York, an alliance of building and construction unions in the New York City area.
Split into simpler sentences: One of the strongest supporters of the president's war policy was Peter J. Brennan. Brennan was president of the Building and Construction Trades Council of Greater New York, an alliance of building and construction unions in the New York City area.