First, it's important to recognize that "sustainability" is a noun and "sustainable" is an adjective.
Sustainability n.
1. the ability to be sustained, supported, upheld, or confirmed.
2. Environmental Science. the quality of not being harmful to the environment or depleting natural resources, and thereby supporting long-term ecological balance, e.g. The committee is developing sustainability standards for products that use energy.
So, in your example:
- a sustainability partner is a person or company or organization that has agreed to work with their other partners to sustain (maintain/keep in good condition) the environment. 'sustainability partners' are two nouns like 'football team' or 'government department'.
- a sustainable partner is a partner that we hope will 'stay/be kept/remain as a partner', just like two people who get married... we hope the husband and wife can stay together.