There is a continuously increasing demand for using High-Performance-Computing (HPC) infrastructure for solving geoscientific questions in different domains. Fostering the "FAIRness" (referring to the FAIR principles of Wilkinson et al. 2016 - "Findable, Accessible, Interoperable, Reusable") of the data generated in HPC calculations is therefore a necessity; however, the sheer size of such data poses a big challenge. In particular, approaches to FAIR data and computing which do not require the complete movevement of extremely big data sets have to be developed. Here, the Interest Group (IG) "High-performance Computing in Earth System Sciences" within NFDI4Earth (the German National Research Data Infrastructure consortium for Earth System Sciences) presents a concept/working paper, which will receive versioned updates as needed. This is intended as an encouragement to both researchers and infrastructure providers to engage in joint discussions on the further design of work processes, future service offerings and their interaction on the background of the FAIR principles for HPC data. The NFDI4Earth IG High-performance Computing in Earth System Sciences will further promote these discussions in NFDI4Earth and bring them into the framework of the entire NFDI. Addendum 2025-02: Updates on the recommendations in this paper have been presented in an addendum paper: https://doi.org/10.5281/zenodo.14796888