Triplet energy transfer (TET) from semiconductor nanocrystals (NCs) has recently emerged as a new triplet sensitization paradigm. It remains unclear how trap states pervasive in NCs influence TET or whether trapped excitons can undergo efficient TET. Here we partially address this issue by studying TET from CuInS2 NCs as a model system because their photogenerated excitons are known to be "self-trapped" due to hole localization to intragap Cu states. We found that, thanks to the long lifetime (209 +/- 17 ns) of self-trapped excitons, they could be extracted with an efficiency of similar to 92.3% by surface-anchored anthracene despite that the TET rate was relatively slow (57.1 +/- 1.7 mu s(-1)). We further leveraged this efficient sensitization to achieve triplet-triplet-annihilation photon upconversion (TTA-UC) with a quantum yield of 18.6 +/- 0.3%. Thus, this study not only demonstrates trapped excitons can undergo efficient TET as well, but also presents the first TTA-UC system sensitized by nontoxic NCs which is important for the real-life application of this technique.