  The astrophysical $S$ factor for the radiative proton capture process on the
$^{15}\mathrm{N}$ nucleus, i.e., $^{15}\mathrm{N}(p, \gamma)^{16}\mathrm{O}$,
at stellar energies are studied within the framework of the cluster effective
field theory. The thermonuclear $^{15}\mathrm{N}(p, \gamma)^{16}\mathrm{O}$
reaction links the type-I to type-II cycles of the carbon-nitrogen-oxygen cycle
and affects the abundances of elements in the univere. For investigating this
reaction in the effective field theory formalism, we first construct an
effective Lagrangian that is appropriate for this reaction at low-energies.
Since the intermediate excited states of the $^{16}\mathrm{O}$ nucleus have a
crucial role in this reaction, we include these resonances in the formalism.
The corresponding radiative capture amplitudes and cross section are
calculated, which lead to the astrophysical $S$ factor. The low energy
constants introduced in the effective Lagrangian are determined by fitting the
theoretical results to the observed $S$ factors in the range of
$130~\mathrm{keV} < E_p < 2500~\mathrm{keV}$ using three different experimental
data sets. Considering the recent data sets, we obtain $S(0) =
29.8\mbox{-}34.1~\mathrm{keV\ b}$, which is in a good agreement with the
estimates from $R$-matrix approaches in the literature. The values of $S$ at
the Gamow energy are found to be larger than $S(0)$ values by about $10\%$.
