  The regularization proposed in [D.~Glavan and C.~Lin, Phys.\ Rev.\ Lett.\
{\bf 124}, 081301 (2020)] led to the black hole solutions which turned out to
be the solutions of the consistent well-defined $4$-dimensional
Einstein-Gauss-Bonnet theory of gravity suggested in [K.~Aoki, M.~Gorji and
S.~Mukohyama, arXiv:2005.03859]. Recently the quasinormal modes of bosonic and
fermionic fields for this theory were studied. Here we calculate quasinormal
frequencies of the test scalar, electromagnetic and Dirac fields for the
spherically symmetric black hole in the novel $4D$ Einstein-Gauss-Bonnet-de
Sitter theory. The values of the quasinormal modes, calculated by the sixth
order WKB method with Pad\'{e} approximants and the time-domain integration,
show that both real oscillation frequency and the damping rate are suppressed
by increasing of the cosmological constant. While the stability of the scalar
and electromagnetic fields follows directly from the positive definiteness of
the effective potential, there is no such positive definiteness for the Dirac
field. Here, with the help of the time domain integration, taking into account
all the modes, we prove stability of the Dirac field in $4D$
Einstein-Gauss-Bonnet-de Sitter theory.
