We report on sensitive new 1.4-GHz VLA radio observations of the pulsar wind nebula G21.5 - 0.9 , powered by PSR J1833 - 1034 , and its environs . Our observations were targeted at searching for the radio counterpart of the shell-like structure seen surrounding the pulsar wind nebula in X-rays . Some such radio emission might be expected as the ejecta from the \stackrel { \textstyle < } { \sim } 1000 yr old supernova expand and interact with the surrounding medium . We find , however , no radio emission from the shell , and can place a conservative 3 \sigma upper limit on its 1-GHz surface brightness of 7 \times~ { } 10 ^ { -22 } W m ^ { -2 } Hz ^ { -1 } sr ^ { -1 } , comparable to the lowest limits obtained for radio emission from shells around other pulsar-wind nebulae . Our widefield radio image also shows the presence of two extended objects of low-surface brightness . We re-examine previous 327-MHz images , on which both the new objects are visible . We identify the first , G21.64 - 0.84 , as a new shell-type supernova remnant , with a diameter of \sim 13′ and an unusual double-shell structure . The second , G21.45 - 0.59 , \sim 1′ in diameter , is likely an H II region .