  Geometrical frustration leads to novel quantum phenomena such as the
spin-liquid phase in triangular and Kagom\'e lattices. Intra-band and
inter-band Fermi surface (FS) nesting can drive unique superconducting (SC)
ground states with $d$-wave and $s^{\pm}$ pairing symmetries, respectively,
according to the criterion that the SC gap changes sign across the nesting
wavevector. For an odd number of FSs, when multiple inter-band nesting is of
comparable strength, the sign-reversal criterion between different FS sheets
can leads to frustration, which promotes novel SC order parameters. Here we
report the experimental observation of a time-reversal symmetry breaking
pairing state in Re$_2$Hf resulting from FS nesting frustration. Furthermore,
our electronic specific heat and transverse-field $\mu$SR experiments suggest a
fully gaped pairing symmetry. The first-principle electronic structure
calculation reveals multiple Fermi surface sheets with comparable inter-band
nesting strength. Implementing the {\it ab-initio} band structure, we compute
spin-fluctuation mediated SC pairing symmetry which reveals a $s+is'$-pairing
state - consistent with experimental observations. Our investigation
demonstrates a novel SC state which provides a putative setting for both
applied and fundamental study.
