The body, which now represents 18 top clubs - including Manchester United and AC Milan - has brought in Glasshouse Partnership on a budget understood to be around £75,000.
The group campaigns in big clubs' interests, for example demanding more compensation for members when players are released for international matches.
G-14 is also appealing to both Uefa and Fifa for 'better management of the international playing calendar'.
G-14's relations with Uefa in particular have historically been fraught - Thellusson said he wanted negotiations with the Swiss-based European football body to be 'constructive'.
Thellusson reports to G-14 general manager Thomas Kurth and will act as spokesman for the Brussels-based organisation.
Glasshouse is also revamping the body's website and 'developing new comms content'.
G-14 formerly used Hill & Knowlton's Brussels office for PA and comms from 2002 to 2004.