There may be several reasons for this behavior.

Firstly, it is possible that in your material several types there are few type of charge carrier with different mobility and concentration and temperature dependence of these values.  Temperature change leads to a change in their relative contributions.

Secondly, in the case of one type of charge carriers such behavior may indicate a hopping conductivity.

What type of material are u testing? The mobility of the charge carriers determine the actual electrical conductivity. But as you know the electrical energy of charge carriers

or a current is a function of temperature. This is actually what is known as the Thompson effect. Hence, generally in actual materials the Seebeck coefficient varies with temperature mainly due to the Thompson effect  which describes the heating or cooling of a current-carrying conductor with a temperature gradient.

Charge concentration based behaviors of thermopower (S) and electrical conductivity (delta) are based on a single material, wherein this does not happen, which is why is the theoretical explanation. This is in fact advantageous for a thermoelectric device (TED) because it may lead to higher figure of merit (i.e. S2x delta/kappa)  provided the associated thermal conductivity (kappa) is also poor. This is considered to be a case of electron-crystal and phonon-glass, which can be expected in a composite and is what normally looking for good TED. Therefore, even if the material in hand may be identified as a single phasic material, it could be a presence of small amount of impurity, that is quite difficult to detect by a simple one/ if the technique to do this is not so accurate, and is most probably making the observed behavior. Then, accordingly the question of involving different mobilities etc could easily be fitted in and be expalined.

Generally, the efficiency of the thermoelectric material depends on the thermoelectric figure-of-merit Z, which is expressed as S2sigma/kappa. In your case, if both S and sigma are increasing in the sense, the thermal conductivity of your material decreasing simultaneously. This may be attributed due to the carrier confinement effect (i.e both electrons and phonons), if your material is a nanostructured material. If you want to interpret more in detail, it is necessary to discuss about, all scattering processes that take place in your material.

Particularly, I think, the behavior of such increase in S and sigma may be due to phonon-drag contribution to the Seebeck coefficient of the material itself. Therefore, I suggest that, it will better if you discuss in detail about the carrier mobility of your material due to lattice scattering (i.e electron-phonon scattering).

Also, the scattering process depends on the type of material, you fabricated. If your material is an alloy semiconductor, then the confinement effect will takes place due to defect-boundary scattering of phonons.

I think, this will help for you.

Dear Sunil could you please provide more details about your question. Is it just generally or do you have an actual measurement to interprete. As Alexander and the other  said there are several reasons way Seebeck and conductivity could increase parallel. You have always to look on your individual system to interpret measurements.

 Dear all, I have a similar question as Sunil kumar, 

But in our case, seebeck coefficient and the electrical conductivity increases together, and carrier concentration also decreases with change in dopant amount. How the defect in the crystal structure can be related to the above variation ??