  In the paper, we investigate the charmed meson rare decay process $D^+ \to
\pi^+\nu\bar\nu$ by using QCD sum rules approach. Firstly, the pion twist-2 and
twist-3 distribution amplitude $\xi$-moments $\langle\xi_{2;\pi}^n\rangle|_\mu$
up to 10th-order and $\langle \xi_{3;\pi}^{(p,\sigma),n}\rangle|_\mu$ up to
fourth-order are calculated by using QCD sum rule under background field
theory. After constructing the light-cone harmonic oscillator model for pion
twist-2, 3 DAs, we get their behaviors by matching the calculated
$\xi$-moments. Then, the $D\to \pi$ transition form factors are calculated by
using QCD light-cone sum rules approach. The vector form factor at large recoil
region is $f_+^{D\to\pi}(0) = 0.627^{+0.120} _{-0.080}$. By taking the rapidly
$z(q^2,t)$ converging simplified series expansion, we present the TFFs and the
corresponding angular coefficients in the whole squared momentum transfer
physical region. Furthermore, we display the semileptonic decay process $\bar
D^0 \to \pi^+ e\bar \nu_e$ differential decay widths and branching fraction
with ${\cal B}(\bar D^0\to\pi^+e\bar\nu_e) = 0.308^{+0.155}_{-0.066} \times
10^{2}$. The $\bar D^0\to\pi^+e\bar\nu_e$ differential/total predictions for
forward-backward asymmetry, $q^2$-differential flat terms and lepton
polarization asymmetry are also given. After considering the non-standard
neutrino interactions, the predictions for the $D^+ \to \pi^+ \nu\bar\nu$
branching fraction is ${\cal B}(D^+ \to \pi^+ {\nu }{\bar\nu}) =
1.85^{+0.93}_{-0.46}\times10^{-8}$.
