Under a scheme called the Veolia cre8 funding challenge, the trust will give grants worth up to £300,000 each to four organisations to set up volunteering schemes that "bring generations together and help to improve health and wellbeing".
Other criteria for applications include demonstrating that the projects will leave a legacy and will allow the volunteers to develop new skills.
Projects must be located within 10 miles of a licensed landfill site.
Margaret Cobbold, executive director of the trust, said: "We have introduced Veolia cre8 to help larger, more creative and ambitious projects that will see volunteers of all ages and backgrounds improve or create public amenities and leave a legacy for everyone to use and enjoy."
The applications process will close on 1 December.
Organisations interested in submitting an application should visit the trust's website for more information.