  We present our works in updating the spin and orbital parameters for the
newly discovered accreting millisecond X-ray pulsar (AMXP) IGR J17591$-$2342
through pulsar timing and analyzing its energy dependent pulse behaviors. The
data being analyzed were collected by Neutron Star Interior Composition
ExploreR (NICER) that observed this AMXP from August to October 2018. Using the
pulse arrival time delay technique, more accurate spin and orbital parameters
were evaluated. From the measured spin frequency derivative, it is estimated
that the magnetic field of the neutron star in IGR J17591$-$2342 is
approximately $4 \times 10^{8}$ G. Precise pulse profiles can be made using the
updated spin and orbital parameters. The soft phase lag phenomenon that is
usually seen in other AMXPs is also observed from $\sim$4 keV to 12 keV with a
value of 0.06 cycles (1.14 $\mu$s). Additionally, the pulsed fractional
amplitude increases from 1 to $\sim$5 keV and then decreases for higher energy
bands. We found that these phenomena, as well as the energy spectrum, can be
explained by the two-component model with a relatively strong blackbody
component and an additional unpulsed disk blackbody component.
