WASHINGTON—Hillary Clinton’s policy advisers wrangled over whether to call for restoring the Glass-Steagall Act, a Depression-era law separating commercial banking and securities activities, according to a new batch of emails released over the past several days by WikiLeaks.

The emails, allegedly obtained from the account of Clinton campaign chairman John Podesta, showed staffers were concerned about how Sen. Elizabeth Warren (D., Mass.) would react if Mrs. Clinton didn’t refer to Glass-Steagall in a planned opinion column...