Inoffensive source of delay in anyone on the move (7)
I believe the answer is:
anodyne
'inoffensive' is the definition.
(I've seen this before)
'source of delay in anyone on the move' is the wordplay.
'source of' suggests taking the first letters.
'in' means one lot of letters goes inside another.
'on the move' is an anagram indicator.
The first letter of 'delay' is 'd'.
'anyone' is an anagram of 'anoyne'.
'd' placed into 'anoyne' is 'ANODYNE'.
(Other definitions for anodyne that I've seen before include "Causing no offence" , "A drug that relieves pain" , "not causing disagreement" , "Relieving hurt" , "Unlikely to cause offence - rather dull" .)