The charity has used Portland PR for the past five years but stopped working with it in December last year. It has since handled the work in-house.
But after a flurry of media coverage this year, the three-strong external relations team is now looking for someone to advise it on a pro-bono basis.
Ideally it is looking for an agency to work eight hours a week, giving media relations and public affairs support, advising the external relations team on literature and assisting at press launches.
Teach First is a programme that trains high-flying graduates as teachers in difficult schools.