Contract element extraction (CEE) is the novel task of automatically identifying and extracting legally relevant elements such as contract dates, payments, and legislation references from contracts. Automatic methods for this task view it as a sequence labeling problem and dramatically reduce human labor. However, as contract genres and element types may vary widely, a significant challenge for this sequence labeling task is how to transfer knowledge from one domain to another, i.e., cross-domain CEE. Cross-domain CEE differs from cross-domain named entity recognition (NER) in two important ways. First, contract elements are far more fine-grained than named entities, which hinders the transfer of extractors. Second, the extraction zones for cross-domain CEE are much larger than for cross-domain NER. As a result, the contexts of elements from different domains can be more diverse. We propose a framework, the Bi-directional Feedback cLause-Element relaTion network (Bi-FLEET), for the cross-domain CEE task that addresses the above challenges. Bi-FLEET has three main components: (1) a context encoder, (2) a clause-element relation encoder, and (3) an inference layer. To incorporate invariant knowledge about element and clause types, a clause-element graph is constructed across domains and a hierarchical graph neural network is adopted in the clause-element relation encoder. To reduce the influence of context variations, a multi-task framework with a bi-directional feedback scheme is designed in the inference layer, conducting both clause classification and element extraction. The experimental results over both cross-domain NER and CEE tasks show that Bi-FLEET significantly outperforms state-of-the-art baselines.