I don't believe VASP has this feature built-in, but you can generate a PROCAR and then use the Python package PYPROCAR to plot the Fermi surface. https://romerogroup.github.io/pyprocar/fermi3D.html I don't think this software can draw plane projections, however.
To complement the nice answer of Prof. Steven Hartman, I can say that you can get an implicit plot of the FS or a sheet of it in a crystallographic plane using the tight-binding approach, for example with ARPES measurements of the fundamental parameters or new exp. techniques.
In addition, you can use a Python script which is very nice or older plot programs with implicit functions tools.
In addition to the answers given above, the Fermi Surface can be obtained using FermiSurfer, it is also possible to plot the surface by following the procedures described in any of the two URLs:
https://www.c2x.org.uk/fermi/qe.html
https://fermisurfer.osdn.jp/en/_build/html/
Note: You have to carry out dense k-points n/scf and bands calculations.
Mahtab Goodarzi you can obtain the Fermi surface through three calculations in Quantum Espresso. You first need to run a default SCF calculation followed by a NSCF (Non-Self-Consistent field) calculation with the occupations turned to "tetrahedra" instead of "smearing". After you run these two calculations you have to run an fs.x calculation, which will generate a .bxsf file where you can plot in XCrysDen for example. Be aware that the K-points are an essential variable to your nscf calculation and a more dense grid will probably give you more accurate results. The fs.x input file is described below:
&fermi
prefix = '...',
outdir = '...'
/
There are other software you can visualize the Fermi surface, but XCrysDen is the one I use for being open-source code, but it is not possible to install it on windows unless you use windows subsystem for Linux or Cygwin to simulate a Linux environment.