Characteristics of supernova remnant G351.7+0.8 and a distance argument against its association with PSR J1721-3532

New images of the supernova remnant (SNR) G351.7+0.8 are presented based on 21cm HI-line emission and continuum emission data from the Southern Galactic Plane Survey (SGPS). SNR G351.7+0.8 has a flux density of 8.4+-0.7 Jy at 1420 MHz. Its spectral index is 0.52+-0.25 (S=v^{-alpha}) between 1420 MHz and 843 MHz, typical of adiabatically expanding shell-like remnants. HI observations show structures possibly associated with the SNR in the radial velocity range of -10 to -18 km/s, and suggest a distance of 13.2 kpc and a radius of 30.7 pc. The estimated Sedov age for G351.7+0.8 is less than 6.8 x 10^{4} yrs. A young radio pulsar PSR J1721-3532 lies close to SNR G351.7+0.8 on the sky. The new distance and age of G351.7+0.8 and recent proper-motion measurements of the pulsar strongly argue against an association between SNR G351.7+0.8 and PSR J1721-3532. There is an unidentified, faint X-ray point source 1RXS J172055.3-353937 which is close to G351.7+0.8. This may be a neutron star potentially associated with G351.7+0.8.