Aspect Sentiment Triplet Extraction (ASTE) has achieved promising results while relying on sufficient annotation data in a specific domain. However, it is infeasible to annotate data for each individual domain. We propose to explore ASTE in the cross-domain setting, which transfers knowledge from a resource-rich source domain to a resource-poor target domain, thereby alleviating the reliance on labeled data in the target domain. To effectively transfer the knowledge across domains and extract the sentiment triplets accurately, we propose a method named Fine-grained cOntrAstive Learning (FOAL) to reduce the domain discrepancy and preserve the discriminability of each category. Experiments on six transfer pairs show that FOAL achieves 6% performance gains and reduces the domain discrepancy significantly compared with strong baselines. Our code will be publicly available once accepted.