Using the HEGRA system of imaging atmospheric Cherenkov telescopes, a region of the Galactic plane (-10° <b <5°, 38° <l <43°) was surveyed for TeV gamma-ray emission, both from point sources and of diffuse nature. The region covered includes 15 known pulsars, 6 known supernova remnants (SNR) and one unidentified EGRET source. No evidence for emission from point sources was detected; upper limits are typically below 0.1 Crab units for the flux above 1 TeV. For the diffuse gamma-ray flux from the Galactic plane, an upper limit of 6.1 × 10-15 ph cm-2 s-1 sr-1 MeV-1 was derived under the assumption that the spatial distribution measured by the EGRET instrument extends to the TeV regime. This upper flux limit is a factor of about 1.5 larger than the flux expected from the ensemble of gamma-ray unresolved Galactic cosmic ray sources.