  1T-TaS$_2$ is a cluster Mott insulator on the triangular lattice with 13 Ta
atoms forming a star of David cluster as the unit cell. We derive a two
dimensional XXZ spin-1/2 model with four-spin ring exchange term to describe
the effective low energy physics of a monolayer 1T-TaS$_2$, where the effective
spin-1/2 degrees of freedom arises from the Kramers degenerate spin-orbital
states on each star of David. A large scale density matrix renormalization
group simulation is further performed on this effective model and we find a
gapless spin liquid phase with spinon Fermi surface at moderate to large
strength region of four-spin ring exchange term. All peaks in the static spin
structure factor are found to be located on the "$2k_F$" surface of half-filled
spinon on the triangular lattice. Experiments to detect the spinon Fermi
surface phase in 1T-TaS$_2$ are discussed.
