  As a successive work to [Phys.Rev.D 102 (2020), 034034], we derive the
$1/m_Q$ corrections to chiral effective Lagrangian for heavy-light mesons from
QCD under proper approximations. The low energy constants in the effective
Lagrangian are expressed in terms of the light quark self-energy and heavy
quark mass $m_Q$. Numerical results of the low energy constants with $1/m_Q$
corrections are given. We find that the results of pion decay constant and the
masses of heavy-light mesons are improved coherently compared to that obtained
in the heavy quark limit.
