  In cosmological group field theory (GFT) models for quantum gravity coupled
to a massless scalar field the total volume, seen as a function of the scalar
field, follows the classical Friedmann dynamics of a flat
Friedmann-Lema\^itre-Robertson-Walker (FLRW) Universe at low energies while
resolving the Big Bang singularity at high energies. An open question is how to
generalise these results to other homogeneous cosmologies. Here we take the
first steps towards studying anisotropic Bianchi models in GFT, based on the
introduction of a new anisotropy observable analogous to the $\beta$ variables
in Misner's parametrisation. In a classical Bianchi I spacetime, $\beta$
behaves as a massless scalar field and can be used as a (gravitational)
relational clock. We construct a GFT model for which in an expanding Universe
$\beta$ initially behaves like its classical analogue before "decaying" showing
a previously studied isotropisation. We support numerical results in GFT by
analytical approximations in a toy model. One possible outcome of our work is a
definition of relational dynamics in GFT that does not require matter.
