Could you please assist me differentiate the above, more so in insulators. Is there a relationship between thermal expansion and thermal conductivity? eg, one being an inverse of the other?
yes, thermal conductivity is the inverse of thermal resistance and thermal expansion is the rate of expansion or contraction of a material with increase in temperature.
Thermal conductivity/resistivity similar to electric conductivity/ resistivity measure the rate of "heat flow' through the material while thermal expansion has no electrical analogue- it is a measure of the change in the dimensions of an object on heating.
For an isotropic homogeneous material, the thermal conductivity in its simplest form might be considered as the inverse of the thermal resistivity. However, for anisotropic heterogeneous material, this could be more complicated than the previous straight forward case. Regarding the thermal expansion, I agree with Dhineshkumar and Bansi.