Complex sentence: Early in 1939, Fleming began an affair with Ann O'Neill (née Charteris), who was married to Baron O'Neill; she was also having an affair with Esmond Harmsworth, the heir to Lord Rothermere, owner of the "Daily Mail".
Split into simpler sentences: Early in 1939 Fleming began an affair with Ann O'Neill (née Charteris), who at the time was married to Baron O'Neill. She was also having an affair with Esmond Harmsworth, the heir to Lord Rothermere, owner of the "Daily Mail".