We investigate numerically the elastic interaction between an eddy-pair and an axisymmetrical cyclonic eddy in inviscid isochoric two-dimensional (2D), as well as in three-dimensional (3D) flows under the quasi-geostrophic (QG) approximation. The eddy-pair is a straight moving Lamb-Chaplygin dipole where the absolute value of either its positive or negative amount of vorticity equals the vorticity of the axisymmetrical eddy. The results for the 2D and 3D cases show that interactions with almost no vorticity exchange or vorticity loss to the background field between ocean eddies, but changing their displacement velocity, are possible. When the eddy-pair approaches the axisymmetrical eddy, their respective potential flows interact, the eddy-pair’s trajectory acquires curvature and their vorticity poles separate. In the QG dynamics, the eddies suffer little vertical deformation, being the barotropic effects dominant. At the moment of highest interaction, the anticyclonic eddy of the pair elongates, simultaneously, the cyclonic eddy of the pair evolves towards spherical geometry, and the axisymmetrical eddy acquires prolate ellipsoidal geometry in the vertically stretched QG space. Once the eddy-pair moves away from the axisymmetrical eddy, its poles close, returning to their original geometry, and the anticyclonic and cyclonic eddy continue as an eddy-pair with a straight trajectory but along a new direction. The interaction is sensitive to the initial conditions and, depending on the initial position of the eddy-pair, as well as on small changes in the vorticity distribution of the axisymmetrical eddy, inelastic interactions may instead occur.