Reliable, informative, and individual uncertainty quantification (UQ) remains missing in current ML community. This hinders the effective application of AI/ML to risk-sensitive domains. Most methods either fail to provide coverage on new data, inflate intervals so broadly that they are not actionable, or assign uncertainties that do not track actual error, especially under a distribution shift. In high-stakes drug discovery, protein-ligand affinity (PLI) prediction is especially challenging as assay noise is heterogeneous, chemical space is imbalanced and large, and practical evaluations routinely involve distribution shift. In this work, we introduce a novel uncertainty quantification method, Trustworthy Expert Split-conformal with Scaled Estimation for Efficient Reliable Adaptive intervals (TESSERA), that provides per-sample uncertainty with reliable coverage guarantee, informative and adaptive prediction interval widths that track the absolute error. We evaluate on protein-ligand binding affinity prediction under both independent and identically distributed (i.i.d.) and scaffold-based out-of-distribution (OOD) splits, comparing against strong UQ baselines. TESSERA attains near-nominal coverage and the best coverage-width trade-off as measured by the Coverage-Width Criterion (CWC), while maintaining competitive adaptivity (lowest Area Under the Sparsification Error (AUSE)). Size-Stratified Coverage (SSC) further confirms that intervals are right-sized, indicating width increases when data are scarce or noisy, and remain tight when predictions are reliable. By unifying Mixture of Expert (MoE) diversity with conformal calibration, TESSERA delivers trustworthy, tight, and adaptive uncertainties that are well-suited to selective prediction and downstream decision-making in the drug-discovery pipeline and other applications.