Which of the following orders of reactivity of acid derivatives towards a nucleophile is correct?

Acid chloride> anhydride> ester is the correct order of reactivity of acid derivatives toward a nucleophile.

Acid Chloride, Acid Anhydride, Ester, and Amide are the order of reactivity for carboxylic acid derivatives. The most reactive acids are acid chlorides, while the least reactive acids are acid amides.
The following group's basicity order is what's to blame for this.

${\mathrm{Cl}}^{-}<\mathrm{R}-{\mathrm{COO}}^{-}<\mathrm{R}-{\mathrm{O}}^{-}<{\mathrm{NH}}_2^{-}$.

Hence, option A is correct.