His name appears frequently in the Brooklyn Daily Eagle chess columns of the 1930s as have been particularly successful in speed tournaments in New York City. His major successes were:
1930-31 - Tied for 2nd-4th in the Marshall Chess Club Championship and tied for 6-7th in the New York State Championship
1936 - 6th in the US Open
1937 - First in the New York State Championship. First in the US Open in Chicago
1938 - Tied for 1st with Frank Marshall in the Marshall Chess Club championship. Tied for 3rd-4th in the US Open. Tied for 6-7th in the US Championship
1940 - Tied for 8-11th in the US Championship
Beyond that little is known. Two birth dates are given. Wikipedia says he was born in 1915 while on chessgamesdotcom his birthday is listed as being June 24, 1908. I believe the 1908 date is likely correct because there was an article in the January 25, 1926 issue of the Brooklyn Daily Eagle stating he was attending City College of New York, so the 1908 birth date would have made him 18 years old at the time. He was also a member of the I.L. Rice Progressive Chess Club of Manhattan.
An interesting post appeared in the Actuarial Outpost forums in 2008 by someone who told of playing an "elderly gentleman" (whom the poster said was, by 2008, long deceased) back in the 1960s who was taking on all comers in the park outside his parents apartment building. The poster stated that over the next two years he played about 20 games against the old gentleman and only beat him once. The man was David Polland.
The poster went on to say that Polland demonstrated a King-Bishop-Knight mate blindfolded without knowledge of opponents exact King move (just whether it was a check or not). Also, according to the poster, Polland was once the 3rd ranked checker player in the world, but I was unable to verify this.
Polland's favorite opening was the English and as mentioned, he shined in rapid play; in one first place finish in a Marshall Chess Club rapid tournament he even defeated Reshevsky, himself a powerful blitz player. On another occasion he held Reshevsky to a draw in a simultaneous.
In following game from the 1940 US Championship Pollard's handling of the opening was weird, but it worked and he was awarded a brilliancy prize for his efforts. Hanauer found his pieces on the Q-side undeveloped and when his pieces in the center were driven off it allowed Polland to begin a sacrificial K-side attack. The attack should not have been decisive, but it was when Hanauer accepted the piece.