Your base class could depend on an interface (or other type) that's injected via the constructor. Your template method(s) could then use the methods on this interface/type to achieve the pattern's desired outcome:
public class BaseClass
{
IDependent _dependent;
public BaseClass(IDependent dependent)
{
_dependent = dependent;
}
public void Alpha() {
_depdendent.Beta();
}
public void Gamma() {
_depdendent.Delta();
}
}
Effectively using composition rather than inheritance.