Randomized clinical trials (RCTs) are the gold standard for producing evidence of treatment effects with high internal validity. Trial results, however, often impact populations that differ from those who enrolled in the trial. Differences between the trial and so-called target population can limit the relevance of trial findings for the target population. Methods in the generalizability and transportability literature aim to produce a treatment effect estimate that applies to a target population of interest. However, in randomized trials, participant non-adherence to the study medication or intervention can dramatically alter the interpretation of transported treatment effect estimates. If non-adherence patterns are expected to differ between the trial participants and those in the target population, the transported effect may no longer reflect the underlying effect of the treatment in the target population. In this work, we develop methods to address these concerns using a principal stratification approach to define subsets of the target population with distinct latent compliance patterns. These subsets form the basis of a transportability problem that we approach using causal inference techniques: defining scientifically-relevant estimands, clarifying necessary identification assumptions, and specifying theory-based estimation and inference techniques. This work addresses some common limitations of RCT data and thus makes such data more useful to clinicians and patients. Our proposed framework can also handle transportation of effects in any principal strata and thus has applicability beyond dealing with non-adherence.