  The accreting millisecond X-ray pulsar Swift J1756.9$-$2508 went into
outburst in April 2018 and June 2019, 8.7 yr after the previous activity
period. We investigated the temporal, timing and spectral properties of these
two outbursts using data from NICER, XMM-Newton, NuSTAR, INTEGRAL, Swift and
Insight-HXMT. The two outbursts exhibited similar broad-band spectra and X-ray
pulse profiles. For the first time, we report the detection of the pulsed
emission up to $\sim100$ keV observed by Insight-HXMT during the 2018 outburst.
We also found the pulsation up to $\sim60$ keV observed by NICER and NuSTAR
during the 2019 outburst. We performed a coherent timing analysis combining the
data from two outbursts. The binary system is well described by a constant
orbital period over a time span of $\sim12$ years. The time-averaged broad-band
spectra are well fitted by an absorbed thermal Comptonization model in a slab
geometry with the electron temperature $kT_{\rm e}=40$-50 keV, Thomson optical
depth $\tau\sim 1.3$, blackbody seed photon temperature $kT_{\rm bb,seed}\sim
$0.7-0.8 keV and hydrogen column density of $N_{\rm H}\sim 4.2\times10^{22}$
cm$^{-2}$. We searched the available data for type-I (thermonuclear) X-ray
bursts, but found none, which is unsurprising given the estimated low peak
accretion rate ($\approx0.05$ of the Eddington rate) and generally low expected
burst rates for hydrogen-poor fuel. Based on the history of four outbursts to
date, we estimate the long-term average accretion rate at roughly
$5\times10^{-12}\ M_\odot\,{\rm yr}^{-1}$ for an assumed distance of 8 kpc. The
expected mass transfer rate driven by gravitational radiation in the binary
implies the source can be no closer than 4 kpc.
