Child's friend with rug in drama, European (8)
I believe the answer is:
playmate
'child's friend' is the definition.
(I've seen this before)
'rug in drama european' is the wordplay.
'rug' becomes 'mat' (both are floor coverings).
'in' means one lot of letters goes inside another.
'drama' becomes 'play' (synonyms).
'european' becomes 'E' (abbreviation e.g. EU).
'play'+'e'='playe'
'mat' inserted inside 'playe' is 'PLAYMATE'.
'with' acts as a link.
(Other definitions for playmate that I've seen before include "Child's companion" , "Child's friend" , "Chum; Ate my pal (anag.)" , "Childhood companion" , "Chum in recreation" .)