In this work, we use flow visualization and rheometry techniques to study the dynamics and evolution of secondary flows in a model wormlike micellar solution sheared between concentric cylinders, i.e., in a Taylor-Couette cell. The wormlike micellar solution studied in this work contains cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal). This system can be shear banding and highly elastic, nonshear banding and moderately elastic, or nearly Newtonian as the temperature is varied over a narrow range. The effect of elasticity on transitions and instabilities is probed by changing the temperature over a wide range of elasticity (El << 1, El approximate to 1, and El >> 1). Elasticity is defined as the ratio of the Weissenberg number to the Reynolds number. For shear banding wormlike micelle solutions where El >> 1, a primary transition from the base Couette flow to stationary vortices that are evenly spaced in the axial direction of the shear cell and are characterized by an asymptotic wave-length is observed. The dimensionless wave-length at the onset of this shear banding transition for CTAB/NaSal system turns out to be much larger than those reported for other shear banding wormlike micelle systems. For the same fluid at a temperature where it shear-thins but does not display shear banding, El approximate to 1, and for slow ramp speeds, the primary transition is to distinct structures that are not stationary but rather travel in the axial direction. At low elasticity (El << 1), where the fluid behaves as a nearly Newtonian fluid, several transitions from purely azimuthal Couette flow to modified Taylor vortex flows and finally chaotic regimes are documented. The behavior in the shear-banding and nonshear-banding regimes are discussed and compared with results in related systems. The possibility of hysteresis in the flow transitions as well as the effects of co-rotation and counter-rotation of the cylinders on transitions and instabilities are also examined for a wide range of elasticity. (C) 2017 The Society of Rheology.