This can be best discussed with reference to periodic table of elements, in which, elements are arranged according to their properties. Bromine and chlorine are arranged in the same group (group 17) and are also known as halogens. One of the common characteristics of elements of this group is the ability to gain an electron to attain the noble gas configuration.
In the periodic table, chlorine is placed above bromine. As one moves down the periodic table, the atomic radius increases, as happens in the case of bromine and chlorine. The reason is the presence of an additional electron shell. Bromine has an atomic number of 35, as compared to chlorine's 17 and has 3d orbital (which is missing in case of chlorine).
Electronic configuration of chlorine is `1s^2, 2s^2, 2p^6, 3s^2, 3p^5`
and that of bromine is `1s^2, 2s^2, 2p^6, 3s^2, 3p^6, 3d^10, 4s^2, 4p^5` .
This extra shell is the reason for the larger atomic radius of bromine as compared to chlorine.
Hope this helps.