Inoffensive European’s boring family (5)
I believe the answer is:
clean
'inoffensive' is the definition.
(thesaurus)
'european's boring family' is the wordplay.
'european' becomes 'E' (abbreviation e.g. EU).
'boring' is an insertion indicator (some letters must 'bore' a hole into other letters).
'family' becomes 'clan' (I've seen this in another clue).
'e' placed inside 'clan' is 'CLEAN'.
(Other definitions for clean that I've seen before include "Completely (colloq.), free of dirt" , "Untarnished" , "Absolute - pure" , "Remove dirt or stain" , "not polluted" .)