We propose a new approach, termed Hybrid DLT, to address a broad range of industrial use cases where certain properties of both private and public DLTs are valuable, while other properties may be unnecessary or detrimental. The Hybrid DLT approach involves a system where private ledgers, with limited data block dissemination, are collaboratively created by nodes within a private network. The Notary, a publicly auditable authoritative component, maintains a single, official, coherent history for each private ledger without requiring access to data blocks. This is achieved by leveraging a public DLT solution to render the ledger histories tamper-proof, consequently providing tamper-evidence for ledger data disclosed to external actors. We present Traent Hybrid Blockchain, a commercial implementation of the Hybrid DLT approach: a real-time, data-intensive collaboration system for organizations seeking immutable data while also needing to comply with the European General Data Protection Regulation (GDPR).