  A new outburst of GX 339$-$4 in 2021 was monitored by the Hard X-ray
Modulation Telescope (\textit{Insight}-HXMT). By using the data of
\textit{Insight}-HXMT from February to March 2021, we make the X-ray timing
analysis of this new outburst. Based on the results of count rates,
hardness-intensity diagram (HID) and power density spectrum (PDS), we confirm
that the source exhibits spectral transitions from the low-hard state (LHS) to
the hard-intermediate state (HIMS). During the transition from the LHS to the
HIMS, Low-frequency Quasi-periodic oscillations (LFQPOs) are detected in the
PDS. We found that these QPOs are all type-C QPOs with centroid frequencies
evolving from $0.1 -0.6$ Hz in the LHS and in the $1 -3$ Hz frequency range in
HIMS. The QPO features above 50 keV are reported for the first time in this
black hole by \textit{Insight}-HXMT. The QPO rms stays stable with time but
decreases with energy at higher energy above $\sim 10$ keV. We also find that
the phase lag of the type-C QPO is close to zero in the early outburst stage,
but becomes positive as the outburst evolves, with a hard lag of $\sim$ 0.6-1.2
rad in $50 -100 $ keV. The implications of the phase lag in high energy bands
and possible physical mechanisms to explain those observations are also
discussed.
