  The gauge singlet right-handed neutrinos (RHNs) are essential fields in
several neutrino mass models that explain the observed eV scale neutrino mass.
We assume RHN field to be present in the vicinity of the electroweak scale and
all the other possible beyond the standard model (BSM) fields arise at high
energy scale $\ge\Lambda$. In this scenario, the BSM physics can be described
using effective field theory (EFT) where the set of canonical degrees of
freedoms consists of both RHN and SM fields. EFT of this kind is usually dubbed
as $N_{R}$-EFT. We systematically construct relevant operators that can arise
at dimension five and six while respecting underlying symmetry. To quantify the
phenomenological implication of these EFT operators we calculate different
couplings that involve RHN fields. We discuss the constraints on these EFT
operators coming from different energy and precision frontier experiments. For
$pp$, $e^{-}p$ and $e^{+}e^{-}$ colliders, we identify various channels which
crucially depends on these operators. We analytically evaluate the decay widths
of RHN considering all relevant operators and highlight the differences that
arise because of the EFT framework. Based upon the signal cross-section we
propose different multi-lepton channels to search for the RHN at 14 TeV LHC as
well as \emph{future} particle colliders.
