Burren chief financial officer Andrew Rose said he had appointed Pelham after a three-way pitch that included GA.
College Hill Associates is also understood to have pitched for the account.
Partner Ben Brewerton declined to comment.
GA started working for Burren in 2003 and handled comms around its stock market flotation in November.
'Every so often we look at our advisers,' Rose said, adding that Pelham, which also works for Premier Oil and First Calgary Petroleums, was selected 'for its expertise in the oil and gas sector'.
Burren Energy, a FTSE 250 company, was criticised by analysts last month for selling part of its stake in the M'Boundi oil field in Congo-Brazzaville to the country's government 'too cheaply'.