  Providing a link between magnetars and radio pulsars, high magnetic field
neutron stars are ideal targets to investigate how bursting/magnetospheric
activity and braking torque variations are connected to rotational glitches.
The last spin-up glitch of the highly magnetised pulsar J1119$-$6127 back in
2007 was the first glitch in a rotationally powered radio pulsar to be
accompanied by radiative changes. Moreover, it was followed by an uncommon
glitch relaxation that resulted in a smaller spin-down rate relative to the
prediction of the pre-glitch timing model. Here, we present 4 years of new
radio timing observations and analyse the total of 16 years of timing data for
this source. The new data uncover an ongoing evolution of the spin-down rate,
thereby allowing us to exclude permanent changes in the external or internal
torque as a stand-alone cause of the peculiar features of the glitch recovery.
Furthermore, no additional variations of the radio pulse profile are detected,
strengthening the association of the previously observed transient emission
features with the glitching activity. A self-consistent measurement of the
braking index yields a value $n\simeq2.7$, indicating a trajectory in the
$P-\dot{P}$ plane inclined towards the magnetars. Such a potential evolutionary
link might be strengthened by a, possibly permanent, reduction of $\sim15\%$ in
$n$ at the epoch of the 2007 glitch.
