$C{l}^{35}$ and $C{l}^{37}$have different valencies.

Both are Isotopes of Chlorine with different mass number due to different number of neutrons but same number of protons. Thus both the atoms have same number of electrons.
The atomic number of Chlorine is 17 hence the electronic configuration is (2, 8, 7). Thus both the atoms have -1 valency as it would have to gain 1 electron and make the outermost shell with 8 electrons to achieve stability as per the Octet rule.

Important tip: Isotopes are atoms with same number of protons, but differing number of neutrons. They are differing forms of a singe element.