  Graphene-based moir\'{e} systems have attracted considerable interest in
recent years as they display a remarkable variety of correlated phenomena.
Besides insulating and superconducting phases in the vicinity of integer
fillings of the moir\'{e} unit cell, there is growing evidence for electronic
nematic order both in twisted bilayer graphene and twisted double-bilayer
graphene (tDBG), as signaled by the spontaneous breaking of the threefold
rotational symmetry of the moir\'{e} superlattices. Here, we combine
symmetry-based analysis with a microscopic continuum model to investigate the
structure of the nematic phase of tDBG and its experimental manifestations.
First, we perform a detailed comparison between the theoretically calculated
local density of states and recent scanning tunneling microscopy data
[arXiv:2009.11645] to resolve the internal structure of the nematic order
parameter in terms of the layer, sublattice, spin, and valley degrees of
freedom. We find strong evidence that the dominant contribution to the nematic
order parameter comes from states at the moir\'{e} scale rather than at the
microscopic scale of the individual graphene layers, which demonstrates the key
role played by the moir\'e degrees of freedom and confirms the correlated
nature of the nematic phase in tDBG. Secondly, our analysis reveals an
unprecedented tunability of the orientation of the nematic director in tDBG by
an externally applied electric field, allowing the director to rotate away from
high-symmetry crystalline directions. We compute the expected fingerprints of
this rotation in both STM and transport experiments, providing feasible ways to
probe it. Rooted in the strong sensitivity of the flat bands of tDBG to the
displacement field, this effect opens an interesting route to the electrostatic
control of electronic nematicity in moir\'{e} systems.
