The agency, which won the retained business - worth fees understood to be in the region of six figures - at the end of last month, is tasked with attracting a new generation of players to the weekly football pools and helping to promote 'Spot the Ball'.
'There is something of a perception that betting on the football pools is for parents and grandparents,' said Brahm managing partner Phil Reed.
'Young people are betting at football games, on the internet and at bookmakers.
Doing the pools is the next logical step for them.
'In the 1970s everyone did the pools - it was part and parcel of the fun of a Saturday evening. We want to get that feeling back,' he added.
Media relations work will target national, regional and local media - 'wherever anyone is talking or writing about football'.
Leeds-based Brahm will also seek to raise awareness of the individuals on the pools panel, a group that includes former footballing greats such as Gordon Banks and Roger Hunt, and which convenes whenever games are postponed.
A four-strong Brahm team is led by account manager Tim Downs, who reports to Littlewoods Leisure PR manager Liz Pendleton.
The brief was formerly held by Stuart Higgins Communications, which lost out in the repitch but continues to work for phone and internet betting arm, Littlewoods Bet Direct.