A critical challenge in analyzing multi-omics data from clinical cohorts is the re-use of these valuable datasets to answer biological questions beyond the scope of the original study. Transfer Learning and Knowledge Transfer approaches are machine learning methods that leverage knowledge gained in one domain to solve a problem in another. Here, we address the challenge of developing Knowledge Transfer approaches to map trans-omic information from a multi-omic clinical cohort to another cohort in which a novel phenotype is measured. Our test case is that of predicting gut microbiome and gut metabolite biomarkers of resistance to anti-TNF therapy in Ulcerative Colitis patients. Three approaches are proposed for Trans-omic Knowledge Transfer, and the resulting performance and downstream inferred biomarkers are compared to identify efficacious methods. We find that multiple approaches reveal similar metabolite and microbial biomarkers of anti-TNF resistance and that these commonly implicated biomarkers can be validated in literature analysis. Overall, we demonstrate a promising approach to maximize the value of the investment in large clinical multi-omics studies by re-using these data to answer biological and clinical questions not posed in the original study.