Given a parametrized Legendrian $\Lambda$ in a contact manifold $(M, \xi)$, there is a well-defined operation called Legendrian surgery, which produces a new contact manifold $(M(\Lambda), \xi(\Lambda))$. The contactomorphism type of the surgered manifold depends only on the Legendrian isotopy class of the initial Legendrian. Given a loop of Legendrians $\Lambda_t$, it is also possible to realize a 1-parameter family of Legendrian surgeries. From this, we naturally obtain a bundle over the circle with fiber $(M(\Lambda), \xi(\Lambda))$. The non-triviality of the bundle depends on the contact isotopy class of a gluing contactomorphism, which we call the “Legendrian surgery contactomorphism.” Its contact isotopy class depends only on the homotopy class of the given loop of Legendrians within the space of parametrized Legendrians. The obvious realization problem is: which contactomorphisms of a given contact manifold are Legendrian surgery contactomorphisms? In this talk, I will address this question by showing that every formally trivial contactomorphism arises as a Legendrian surgery contactomorphism associated with a certain loop of Legendrians in some overtwisted contact manifold with controlled topology. As a consequence, in 3-dimensional contact topology, we will deduce the existence of formally contractible but non-contractible loops of loose Legendrians in every overtwisted contact 3-manifold. This is a joint work in progress with Fabio Gironella.