ICORELEVEL = 1 | 2
VASP supports two options to calculate changes in the core level energies. A detailed documentation of the implementation is presently missing, we however refer to  and references therein for a overview.
The simpler option (ICORELEVEL = 1) calculates the core levels in the initial state approximation, which just involves recalculating the KS eigenvalues of the core states after a self-consistent calculation of the valence charge density. ICORELEVEL = 1 is a little bit more involved than the calculations using LVTOT = .TRUE., since the Kohn-Sham energy of each core state is recalculated. This adds very little extra cost to the calculations; usually the shifts correspond very closely to the change of the electrostatic potential at the lattice sites (calculated using LVTOT = .TRUE.).
The second option (ICORELEVEL = 2) is more involved. In this case, electrons are removed from the core and placed into the valence (effectively increasing NELECT). The vasp implementation excited all selected core electrons for all atoms of one species. The species as well as the selected electrons are specified using
CLNT = species CLN = main quantum number of excited core electron CLL = l quantum number of excited core electron CLZ = electron countThe electron count specifies how many electrons are excited from the core. Usually 1 or 0.5 (Slaters transition state) are sensible choices. CLNT selects for which species in the POTCAR file the electrons are excited. Usually one would like to excite the electrons for only one atom, this requires to change the POSCAR and POTCAR file, such that the selected atom corresponds to one species in the POTCAR file. i.e. if the calculation invokes a supercell with 64 atoms of one type, the selected atom needs to be singled out, and the POSCAR file will than contain 63 ``standard'' atoms as well as one special species, at which the excited core hole will be placed (the POTCAR file will hold two identical PAW datasets in this case).
Several caveats apply to this mode. First the excited electron is always spherical, multipole splitting are not available. Second, the other core electrons are not allowed to relax, which might cause a slight error in the calculated energies. Third, absolute energies are not meaning full, since VASP usually reports valence energies only. Only relative shifts of the core electron binding energy are relevant (in some cases, the VASP total energies might become even positive).