Shown in the figure is a shell made of a conductor. It has inner radius $\text{'}a\text{'}$ and outer radius '$b$', and carries charge $\text{'}Q\text{'}$. At its centre a dipole $\overrightarrow{p}$, as shown. In this case

 

As the electric dipole creates non-uniform electric field inside the conductor, there will be a non-uniform charge induced on the inner surface.

As the dipole possesses both positive and negative charges. The net charge inside the shell is zero.  So the induced charge on the outer surface$=0$

So no field will be created outside the shell due to electric dipole.  Electric field will be created only by charge $Q$ that it carries. Thus electric field outside the shell

$E=\frac{kQ}{r^2}$