Some novel physical consequences of the Extended Relativity Theory in $C$-spaces (Clifford spaces) were explored recently. In particular, generalized photon dispersion relations allowed for energy-dependent speeds of propagation while still $retaining$ the Lorentz symmetry in ordinary spacetimes, but breaking the $extended$ Lorentz symmetry in $C$-spaces. In this work we analyze in further detail the extended Lorentz transformations in Clifford Space and their physical implications. Based on the notion of ``extended events" one finds a very different physical explanation of the phenomenon of ``relativity of locality" than the one described by the Doubly Special Relativity (DSR) framework. A generalized Weyl-Heisenberg algebra, involving polyvector-valued coordinates and momenta operators, furnishes a realization of an extended Poincare algebra in $C$-spaces. In addition to the Planck constant $\hbar$, one finds that the commutator of the Clifford scalar components of the Weyl-Heisenberg algebra requires the introduction of a $dimensionless$ parameter which is expressed in terms of the ratio of two length scales : the Planck and Hubble scales. We finalize by discussing the concept of ``photons", null intervals, effective temporal variables and the addition/subtraction laws of generalized velocities in $C$-space.