The importance of shocks in nova explosions has been highlighted by Fermi's discovery of \gamma-ray producing novae. Over three years of multi-band VLA radio observations of the 2010 nova V1723 Aql show that shocks between fast and slow flows within the ejecta led to the acceleration of particles and the production of synchrotron radiation. Soon after the start of the eruption, shocks in the ejecta produced an unexpected radio flare, resulting in a multi-peaked radio light curve. The emission eventually became consistent with an expanding thermal remnant with mass \(2 \times 10^{-4} M_\odot\) and temperature \(10^4\) K. However, during the first two months, the \(\gtrsim 10^6\) K brightness temperature at low frequencies was too high to be due to thermal emission from the small amount of X-ray producing shock-heated gas. Radio imaging showed structures with velocities of 400 km s\(^{-1}\) (d/6 kpc) in the plane of the sky, perpendicular to a more elongated 1500 km s\(^{-1}\) (d/6 kpc) flow. The morpho-kinematic structure of the ejecta from V1723 Aql appears similar to nova V959 Mon, where collisions between a slow torus and a faster flow collimated the fast flow and gave rise to \gamma -ray producing shocks. Optical spectroscopy and X-ray observations of V1723 Aql during the radio flare are consistent with this picture. Our observations support the idea that shocks in novae occur when a fast flow collides with a slow collimating torus. Such shocks could be responsible for hard X-ray emission, \gamma -ray production, and double-peaked radio light curves from some classical novae.