As my question indicated, I would like to perform carrier (electron-hole) doping. Could you please guide to the right method using VASP ?
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NELECT tag should do the trick. A number that's larger than the default value (which is automatically calculated by VASP to be the number of valence electrons in the system) gives you charge doping and a real number that's lower than the default value gives you hole doping.
Note that one doesn't necessarily needs to do a normal calculation to know the default NELECT value. It can be calculated manually by checking the number of valence electrons for each element in the POTCAR file and multiply that number of electrons with the number of corresponding atoms in the POSCAR.
Carrier concentration can be calculated by calculate the number of carrier you added/substracted (call it $\Delta N_\text{elect}$) divided by the volume of the unit cell ($V_\text{cell}$).
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$\begingroup$ To avoid things getting too long here, I moved this discussion to the VASP chatroom $\endgroup$– Tyberius ♦Oct 8, 2021 at 18:15