  We discovered 2.8 s pulsations in the X-ray emission of the ultraluminous
X-ray source (ULX) M51 ULX-7 within the UNSEeN project, which was designed to
hunt for new pulsating ULXs (PULXs) with XMM-Newton. The pulse shape is
sinusoidal and large variations of its amplitude were observed even within
single exposures (pulsed fraction from less than 5% to 20%). M51 ULX-7 is a
variable source, generally observed at an X-ray luminosity between $10^{39}$
and $10^{40}$ erg s$^{-1}$, located in the outskirts of the spiral galaxy M51a
at a distance of 8.6 Mpc. According to our analysis, the X-ray pulsar orbits in
a 2-d binary with a projected semi-major axis $a_\mathrm{X} \sin i \simeq$ 28
lt-s. For a neutron star (NS) of 1.4 $M_{\odot}$, this implies a lower limit on
the companion mass of 8 $M_{\odot}$, placing the system hosting M51 ULX-7 in
the high-mass X-ray binary class. The barycentric pulse period decreased by
$\simeq$0.4 ms in the 31 d spanned by our May -- June 2018 observations,
corresponding to a spin-up rate $\dot{P} \simeq -1.5\times10^{-10}\text{s
s}^{-1}$. In an archival 2005 XMM-Newton exposure, we measured a spin period of
$\sim$3.3 s, indicating a secular spin-up of $\dot{P}_{\mathrm{sec}}\simeq
-10^{-9}\text{ s s}^{-1}$, a value in the range of other known PULXs. Our
findings suggest that the system consists of an OB giant and a moderately
magnetic (dipole field component in the range $10^{12}$ G $\lesssim
B_{\mathrm{dip}}\lesssim 10^{13}$G) accreting NS with weakly beamed emission
($1/12\lesssim b\lesssim1/4$).
