When chlorine and bromine come together, they form a covalent bond. This is because they both have a similar electronegativity, and the difference is not large enough to form an ionic bond.
More specifically, they will form a nonpolar covalent bond. This is because the electronegativity difference between chlorine and bromine is very small (Cl: 3.16, Br: 2.96). This means that the electrons in the bond are shared almost equally between the two atoms, resulting in a nonpolar molecule.