We used the OSIRIS camera at the 10.4 m Gran Telescopio Canarias (GTC) to monitor the astrometric motion of the L4.5 dwarf 2M1821$+$14 over 17 months. The astrometric residuals of eleven epochs have a r.m.s. dispersion of 0.4 mas, which is larger than the average precision of 0.23 mas per epoch and hints towards an additional signal or excess noise. Comparison of the point-spread-functions in OSIRIS and FORS2/VLT images reveals no differences critical for high-precision astrometry, despite the GTCs segmented primary mirror. We attribute the excess noise to an unknown effect that may be uncovered with additional data. For 2M1821$+$14, we measured a relative parallax of $106.15 pm 0.18$ mas and determined a correction of $0.50pm0.05$ mas to absolute parallax, leading to a distance of $9.38 pm0.03$ pc. We excluded at 3-$sigma$ confidence the presence of a companion to 2M1821$+$14 down to a mass ratio of 0.1 ($approx 5, M_mathrm{Jupiter}$) with a period of 50--1000 days and a separation of 0.1--0.7 au. The accurate parallax allowed us to estimate the age and mass of 2M1821$+$14 of 120--700 Myr and 0.049$^{+0.014}_{-0.024}$ M$_odot$, thus confirming its intermediate age and substellar mass. We complement our study with a parallax and proper motion catalogue of 587 stars ($isimeq15.5-22$) close to 2M1821$+$14, used as astrometric references. This study demonstrates sub-mas astrometry with the GTC, a capability applicable for a variety of science cases including the search for extrasolar planets and relevant for future astrometric observations with E-ELT and TMT.
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