  We extend the investigation of the Generalized Parton Distribution for a
charged pion within a fully covariant constituent quark model, in two respects:
(i) calculating the tensor distribution and (ii) adding the treatment of the
evolution, needed for achieving a meaningful comparison with both the
experimental parton distribution and the lattice evaluation of the so-called
generalized form factors. Distinct features of our phenomenological covariant
quark model are: (i) a 4D Ansatz for the pion Bethe-Salpeter amplitude, to be
used in the Mandelstam formula for matrix elements of the relevant current
operators, and (ii) only two parameters, namely a quark mass assumed to hold
$m_q=~220$ MeV and a free parameter fixed through the value of the pion decay
constant. The possibility of increasing the dynamical content of our covariant
constituent quark model is briefly discussed in the context of the Nakanishi
integral representation of the Bethe-Salpeter amplitude.
