An apparatus and method are provided for performing a vector rearrangement operation as data elements are moved between memory and vector registers. The apparatus has processing circuitry for performing operations specified by a sequence of program instructions, and a set of vector registers, where each vector register is arranged to store a vector comprising a plurality of data elements. The processing circuitry includes access circuitry to move the data elements between memory and multiple vector registers of the set, and to perform a rearrangement operation as the data elements are moved so that the data elements are arranged in a first organisation in the memory and are arranged in a second, different, organisation in the vector registers. Decode circuitry is arranged to be responsive to a group of rearrangement instructions within the sequence of program instructions to produce control signals to control execution of each rearrangement instruction by the processing circuitry. Each rearrangement instruction in the group defines a data element access pattern that differs to the data element access pattern defined by each other rearrangement instruction in the group, and that causes the access circuitry to access more than one vector register amongst the multiple vector registers involved in the rearrangement operation. Through such an approach, the access circuitry performs the rearrangement operation as a result of the processing circuitry executing all of the rearrangement instructions in the group. The use of such a group of rearrangement instructions can enable an efficient performance of the rearrangement operation by reducing stalling within the apparatus that might otherwise occur if all of the required steps to be performed to implement the rearrangement operation were implemented in response to execution of a single instruction.