Red clover (Trifolium pratense) is a perennial forage legume wildly used in temperate regions, including northern Europe. Its breeders are under increasing pressure to obtain rapid genetic gains to meet the high demand for improved forage yield and quality. One solution to increase genetic gain by reducing time and increasing accuracy is genomic selection. Thus, efficient genomic prediction (GP) models need to be developed, which are unbiased to traits and harvest time points. This study aimed to develop and evaluate single-trait (ST) and multi-trait (MT) models that simultaneously target more than one trait or cut. The target traits were dry matter yield, crude protein content, net energy for lactation, and neutral detergent fiber. The MT models either combined dry matter yield with one forage quality trait, all traits at one cut, or one trait across all cuts. The results show an increase with MT models where the traits had a genetic correlation of 0.5 or above. This study indicates that non-additive genetic effects have significant but varying effects on the predictive ability and reliability of the models. The key conclusion of this study was that these non-additive genetic effects could be better described by incorporating genetically correlated traits or cuts.