Not stopping with others to accept errand, oddly (7)
I believe the answer is:
eternal
'not stopping' is the definition.
(going on forever)
'with others to accept errand oddly' is the wordplay.
'with others' becomes 'et al' (short for 'et alia', Latin for 'and others').
'to accept' indicates putting letters inside.
'oddly' means one should take alternating letters (letters in the odd-numbered positions are used).
The alternating letters of 'errand' are 'ern'.
'etal' going around 'ern' is 'ETERNAL'.
(Other definitions for eternal that I've seen before include "Valid for all time" , "with lasting benefit" , "Ceaseless" , "like Rome?" , "Forever or unchanging" .)