Answer
Iron or $Fe$
Work Step by Step
The metal in the activity series that is oxidized with $Ni^{2+}$ ions but not $Cr^{3+}$ ions is Iron because it's in between Nickel and Chromium. $Fe$ is above $Ni$ so it can be oxidized with $Ni^{2+}$ but it's below $Cr^{3+}$ so it can't be oxidized with $Cr^{3+}$.