Recent investigations of exotic nuclei with $N=32$ and $34$ have highlighted the presence of sizable subshell closures at these neutron numbers that are absent in stable isotones. Indeed, the development of the shell gap at $N=32$ is now well established from studies along the calcium, titanium, and chromium isotopic chains and, more recently, below the $Z=20$ core in potassium and argon isotones. The onset of a new subshell closure at $N=34$ was reported in $^{54}$Ca owing to the relatively high energy of its first $2^{+}$ state. On the theoretical side, the development of these neutron subshell gaps has been discussed, for example, in the framework of tensor-force-driven shell evolution; as protons are removed from the $\pi f_{7/2}$ orbital, the $\nu f_{5/2}$ state becomes progressively less bound and shifts up in energy relative to the $\nu p_{3/2}$--$\nu p_{1/2}$ spin-orbit partners. However, it was also reported that no significant $N=34$ subshell gap exists in titanium, despite the fact that an inversion of the $\nu f_{5/2}$ and $\nu p_{1/2}$ orbitals has been noted. Thus, the strength of the $N=34$ subshell closure in the scandium isotopes, which lie between calcium and titanium, provides additional insight on the migration of the $\nu f_{5/2}$ orbital in exotic nuclei. In the present work, the low-lying structures of the neutron-rich isotopes $^{54}$Sc, $^{55}$Sc, and $^{56}$Sc---investigated using in-beam $\gamma$-ray spectroscopy with fast radioactive projectiles---will be presented, and the evolution of the $N=34$ subshell closure will be further examined. The results will be compared to modern shell-model calculations applied within the $pf$ shell.