The phrase "to represent the club" means to act or speak on behalf of the club, making sure its values and interests are shown in a positive way. Full definition
Some have even joined us to represent the club in the alumni category of competitions! (sport.ox.ac.uk)
It is significant how the candidate represents the club, and that it is a person who gives youth a chance. (express.co.uk)
The manager should have gotten everyone together immediately after the season ended and say if you down want to represent this club anymore get with me now so we can start looking for replacements. (justarsenal.com)