How would you explain the lower atomic radius of $Ga$ as compared to $Al$ ?

Although $Ga$ has one shell more than $\mathrm{Al}$, its size is lesser than $\mathrm{Al}$. This is because of the poor shielding effect of the $3 d$-electrons. The shielding effect of $d$-electrons is very poor and the effective nuclear charge experienced by the valence electrons in gallium is much more than it is in the case of $\mathrm{Al}$.