The trade body for councils is now recruiting for a director of corporate strategy and public affairs who will report to recently recruited CEO Paul Coen.
Muirhead's director of strategy title has been tweaked to better represent the brief.
The post now has greater focus on stakeholder relations, particularly since the LGA's introduction of its Reputation campaign.
The former Ministry of Defence director of information has been on secondment at the LGA for the past year and a half but will now move on.
She will remain in the post until a replacement is found.
‘The post has been reconfigured to put greater emphasis on external relations. I am considering opportunities,' said Muirhead, who oversees a team of 30 at the organisation.
Muirhead joined the LGA in April 2005 (PRWeek, 14 January 2005). She was previously director of modernising rural delivery at the Department for the Environment, Food and Rural Affairs.
The LGA launched its Reputation project, designed to overhaul the image of local government and help the LGA lobby for greater devolved power, last year.
Its media and campaigns programme director is Edward Welsh, who oversees the LGA's news operation. Richard Stokoe remains chief media officer.