Staite joined B-M's lobbying practice earlier this year (PRWeek, 29 July) after seven years in a number of policy and communications roles with the Tories.
Staite's most recent role at Conservative Party HQ was head of regional media.
Earlier this year he was seconded to work for Boris Johnson as communications adviser during Johnson's successful London Mayoral campaign.
This week it emerged he has joined Fleishman-Hillard's corporate comms and issues management team as an account director.
It is understood that Staite walked out of B-M before completing his probation period.
In the new role, he will report to Gavin Megaw, head of corporate comms and issues management.