Display screen or portion thereof with animated card communication interface

FIG. 1 is a first image in a sequence for a display screen or portion thereof with animated card communication interface showing the new design;

FIG. 2 is a second image thereof; and,

FIG. 3 is a third image thereof.

The appearance of the animated images sequentially transitions between the images shown in FIGS. 1 through 3 .

The process or period in which one image transitions to another forms no part of the claimed design.

The broken lines showing a display screen or portion thereof and all other broken lines showing portions of an animated card communication interface shown in FIGS. 1 through 3 illustrate environmental subject matter and form no part of the claimed design. The broken lines forming a communication device shown in FIGS. 1 through 3 illustrate environmental subject matter and form no part of the claimed design.