Aerial image sequences of an ebbing river plume propagating into a tidal cross‐flow demonstrate the presence of along‐front instabilities at multiple scales, which appear to propagate along‐front in the direction of the shear flow. We hypothesize the instabilities are due to cross‐front shear in the along‐front velocity field. Image analysis quantifies the horizontal shear across the plume front as well as the length scales and propagation speeds of the instabilities. In situ measurements from cross‐front ship transects are also used to examine shear and the width of the shear layer. A non‐hydrostatic numerical simulation of an ebb plume in an idealized tidal cross‐flow was conducted using comparable flow parameters and confirms the presence of shear instabilities. An additional numerical simulation without a tidal‐cross flow demonstrates that shear instabilities are not present; rather, lobe‐and‐cleft structures on the nose of the gravity current emerge. According to the scaling of White and Helfrich (2013), utilizing both the observed and modeled parameters, it is shown that shear instabilities are likely in the observed and modeled cross‐flow scenario, and confirms that they are unlikely to emerge in the no cross‐flow model case. Plain Language Summary Where rivers discharge into the ocean, distinct fronts form between the fresher river and more saline ocean waters. Fluid instabilities often form along these fronts. The dynamics of these frontal structures can be complicated, and influence the river plume during its life cycle. Here, we present unique observations of horizontal instabilities that develop along an ebbing river plume, and propagate along the front of the plume like waves. We analyze these instabilities for their spatial and temporal characteristics, and use a model forced with similar flow properties to see if such instabilities can be simulated. Key Points Novel observations of frontal instabilities on an ebbing plume are presented and their speeds and length scales are quantified Non‐hydrostatic modeling of a plume ebbing into a tidal cross‐flow demonstrates similar shear instabilities Modeling also confirms instability vs. gravity current behavior using a non‐dimensional parameter characterization