Any club or membership organisation can help people to get together with similar interests. Postdoctoral associations exist locally within research institutions and universities (see if there is one where you work), as well as at the national level and even at the international level. If you can’t find one relevant or accessible to your needs, try looking for other organisations such as learned societies, professional associations related to your disciplinary interests or alumni groups.
Here is a list of some of the postdoctoral associations I know about. You may know of others:
International Consortium of Research Staff Assocations (iCORSA);
World Association of Young Scientists
National Postdoctoral Association (USA)
Research Staff Associations in the UK
Irish Research Staff Association
Association National of Doctors (France)