The maximum covalency that iodine can exhibit is____________

Because iodine has seven valence electrons, it usually only forms one covalent bond.

An example is $\mathrm{H}-\mathrm{I}$.
Highly electronegative elements such as fluorine, chlorine, and oxygen, on the other hand, can cause iodine to form 3, 5, or 7 covalent bonds.
Examples are ${\mathrm{IF}}_3,{\mathrm{IF}}_5$, and ${\mathrm{IF}}_7$.

Hence the required answer is 7.