Sir Denis O'Connor, outgoing HM Chief Inspector of Constabulary, will give evidence on Olympics security.
Stephen Greenhalgh, Deputy Mayor of London for Policing and Crime, will give evidence on policing in London.
Metropolitan Police Commissioner Bernard Hogan-Howe has also been asked to give oral evidence.
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Greater Manchester Police said "inquiries are ongoing to fully understand the circumstances of the incident."
The US president enjoyed rousing support for his political agenda as a formerly hostile audience cheered his plans in office to the rafters.
The former leader said the party needed to learn lessons after his successor Paul Nuttall failed to unseat Labour in a hard-fought campaign.