  We show that short-range resonating-valence-bond correlations and long-range
order can coexist in the ground state (GS) of a frustrated spin system. Our
study comprises a comprehensive investigation of the quantum magnetism on the
structurally disorder-free single crystal of Cu$_2$(OH)$_3$NO$_3$, which
realizes the $s$ = 1/2 Heisenberg model on a spatially anisotropic triangular
lattice. Competing exchange interactions determined by fitting the
magnetization measured up to 55 T give rise to an exotic GS wavefunction with
coexistence of the dominant short-range resonating-valence-bond correlations
and weak long-range stripe order (ordered moment $M_0$ = $|\langle
s_i^z\rangle|$ $\sim$ 0.02). At low temperatures, a first-order spin-flop
transition is visible at $\sim$ 1-3 T. As the applied field further increases,
another two magnetic-field-induced quantum phase transitions are observed at
$\sim$ 14-19 and $\sim$ 46-52 T, respectively. Simulations of the Heisenberg
exchange model show semi-quantitative agreement with the magnetic-field
modulation of these unconventional phases, as well as the absence of visible
magnetic reflections in neutron diffraction, thus supporting the GS of the spin
system of Cu$_2$(OH)$_3$NO$_3$ may be approximate to a quantum spin liquid. Our
study establishes structurally disorder-free magnetic materials with spatially
anisotropic exchange interactions as a possible arena for spin liquids.
