The phrase "predecessor organisations" refers to the organizations that existed before the current one. They are the earlier or previous versions of the organization, with a similar purpose or function. Full definition
Hundreds of students have been supported through MLA and its predecessor organisations since 1975. (mla.com.au)
In those previous cases, radical groups such as Islamic State and its predecessor organisations took full advantage of the chaos caused by lack of central authority and the resulting civil strife. (politics.co.uk)
Astute observers of the current situation in Syria will see parallels between the current state of Islamic State and its predecessor organisations in Iraq. (politics.co.uk)