  We present LOFAR observations at 150 MHz of the borderline FRI/FRII giant
radio galaxy NGC 6251. This paper presents the most sensitive and
highest-resolution images of NGC 6251 at these frequencies to date, revealing
for the first time a low-surface-brightness extension to the northern lobe, and
a possible backflow associated with the southern lobe. The integrated spectra
of components of NGC 6251 are consistent with previous measurements at higher
frequencies, similar to results from other LOFAR studies of nearby radio
galaxies. We find the outer structures of NGC 6251 to be either at
equipartition or slightly electron dominated, similar to those of FRII sources
rather than FRIs; but this conclusion remains tentative because of
uncertainties associated with the geometry and the extrapolation of X-ray
measurements to determine the external pressure distribution on the scale of
the outer lobes. We place lower limits on the ages of the extension of the
northern lobe and the backflow of the southern lobe of $t \gtrsim 250$ Myr and
$t \gtrsim 210$ Myr respectively. We present the first detection of
polarisation at 150 MHz in NGC 6251. Taking advantage of the high Faraday
resolution of LOFAR, we place an upper limit on the magnetic field in the group
of $B < 0.2 (\Lambda_B / 10 {\rm kpc})^{-0.5} \mu$G for a coherence scale of
$\Lambda_B < 60 {\rm kpc}$ and $B < 13 \mu$G for $\Lambda_B = 240$ kpc.
