  We study a Lie algebra type $\kappa$-deformed space with undeformed rotation
algebra and commutative vector-like Dirac derivatives in a covariant way. Space
deformation depends on an arbitrary vector. Infinitely many covariant
realizations in terms of commuting coordinates of undeformed space and their
derivatives are constructed. The corresponding coproducts and star products are
found and related in a new way. All covariant realizations are physically
equivalent. Specially, a few simple realizations are found and discussed. The
scalar fields, invariants and the notion of invariant integration is discussed
in the natural realization.
