I verified that this is error happens

solved by:
ln -sf /usr/lib/x86_64-linux-gnu/libvolk.so.1.3.1 /usr/lib/x86_64-linux-gnu/libvolk.so.1.3

works

dpkg --status gqrx-sdr
Package: gqrx-sdr
Status: install ok installed
Priority: optional
Section: hamradio
Installed-Size: 2172
Maintainer: A. Maitland Bottoms <[email protected]>
Architecture: amd64
Version: 2.9-2
Replaces: gqrx (<= 2.3.0-0kali4)
Depends: pulseaudio, libboost-program-options1.62.0, libboost-system1.62.0, libc6 (>= 2.14), libgcc1 (>= 1:4.0), libgnuradio-analog3.7.11, libgnuradio-audio3.7.11, libgnuradio-blocks3.7.11, libgnuradio-digital3.7.11, libgnuradio-fft3.7.11, libgnuradio-filter3.7.11, libgnuradio-osmosdr0.1.4 (>= 0.1.4-13), libgnuradio-pmt3.7.11, libgnuradio-runtime3.7.11, liblog4cpp5v5, libpulse0 (>= 0.99.1), libqt5core5a (>= 5.9.0~beta), libqt5gui5 (>= 5.2.0), libqt5network5 (>= 5.0.2), libqt5svg5 (>= 5.6.0~beta), libqt5widgets5 (>= 5.2.0~alpha1), libstdc++6 (>= 5.2), libvolk1.3
Conflicts: gqrx (<= 2.3.0-0kali4)
Description: Software defined radio receiver
Gqrx supports many of the SDR hardware available, including Funcube
Dongles, rtl-sdr, HackRF and USRP devices.
.
Includes AM, SSB, FM-N and FM-W (mono and stereo) demodulators, and
Special FM mode for NOAA APT. Displays FFT plot and spectrum waterfall.
.
It is powered by GNU Radio and the Qt GUI toolkit.
Homepage: http://gqrx.dk/
root@shoe:~# gqrx
gqrx: error while loading shared libraries: libvolk.so.1.3: cannot open shared object file: No such file or directory

Very easy to fix, but doesn't work out-of-the-box. Any chance we get this fixed with a new libvolk package?

kali-rolling currently has gqrx-sdr 2.11.5-1 which depends on libvolk1.4 which contains libvolk.so.1.4 so I believe that this is now a non-issue.

Please confirm that the latest version works out of the box for you.

Yes, after latest (today) update it does work by default. Thanks !