Can directional natural selection occur for a complex trait?

I's say no because a complex trait is usually governed by multiple genes. Directional selection alone would be unlikely to maintain polymorphism at multiple loci.

Directional selection occurs when the environment of a population is changing in some definitive way. This usually means that one extreme for the frequency distribution for some traits gradually becomes less adaptive as the environment changes and is selected against. Provided the population has sufficient variability and the change is not too rapid, the result will normally be to shift the frequency distribution in a direction that is adaptive relative to the changing conditions. The development of insecticide-resistant populations of insects or antibiotic resistance in bacteria is two example of directional selection. If the change is very rapid, the population has low genetic/phenotypic variability, or another species is available that is already well-adapted to the changing environment, the population is question may well be excluded or restricted as a result of the changing conditions. Directional selection can cause the evolution of a species with time, but does not increase bio-diversity.