Answer is: yes, reaction occurs.
Reactivity series is an empirical progression of a series of metals, arranged by their reactivity from highest to lowest (alkaline metals have highest reactivity and Noble metals lowest reactivity).
Metal higher in the reactivity series will displace another, zinc is more reactive than nickel.
Chemical reaction: Zn(s) + NiCl₂(aq) → ZnCl₂(aq) + Ni(s).
Ionic reaction: Zn(s) + Ni²⁺(aq) + 2Cl⁻(aq) → Zn²⁺(aq) + 2Cl⁻(aq) + Ni(s).
Net ionic reaction: Zn(s) + Ni²⁺(aq) → Zn²⁺(aq) + Ni(s).
Zinc metal is oxidized (from oxidation number 0 to +2) and nickel is reduced (from oxidation number +2 to 0).