An electric dipole is placed in an electric field generated by a point charge.

Generally the electric field due to the point charge is $E=kq/r^2$ and dipole moment is $p=qr$
Force on the dipole is $\vec{F}=(\vec{p}.\vec{\nabla })\vec{E}\ne 0$ always in this case.
Torque on the dipole $\vec{\tau }=\vec{p}\times \vec{E}$
if the dipole moment and the electric field are parallel to each other, then the torque may be zero because $pE\sin 0=0$