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Most genetic variants associated with complex traits and diseases occur in non-coding genomic regions and are hypothesized to regulate gene expression. To understand the genetics underlying gene expression variability, we characterize 14,324 ancestrally diverse RNA-sequencing samples from the NHLBI Trans-Omics for Precision Medicine (TOPMed) program and integrate whole genome sequencing data to perform and expression and splicing quantitative trait locus (-/trans-e/sQTL) analyses in six tissues and cell types, most notably whole blood (N=6,454) and lung (N=1,291). We show this dataset enables greater detection of secondary cis-e/sQTL signals than was achieved in previous studies, and that secondary cis-eQTL and primary trans-eQTL signal discovery is not saturated even though eGene discovery is. Most TOPMed trans-eQTL signals colocalize with cis-e/sQTL signals, suggesting many trans signals are mediated by cis signals. We fine-map European UK BioBank GWAS signals from 164 traits and colocalize the resulting 34,107 fine-mapped GWAS signals with TOPMed e/sQTL signals, finding that of 10,611 GWAS signals with a colocalization, 7,096 GWAS signals colocalize with at least one secondary e/sQTL signal. These results demonstrate that larger e/sQTL analyses will continue to uncover secondary e/sQTL signals, and that these new signals will benefit GWAS interpretation.