Turkey welcomed into swelling European project (8)
I believe the answer is:
protrude
'project' is the definition.
('protrude' can be a synonym of 'project')
'turkey welcomed into swelling european' is the wordplay.
'turkey' becomes 'tr' (I've seen this in other clues).
'welcomed into' means one lot of letters goes inside another.
'swelling' becomes 'proud' (proud can mean swelling or jutting out).
'european' becomes 'e' (abbreviation e.g. EU).
'tr' put into 'proud' is 'protrud'.
'protrud'+'e'='PROTRUDE'
(Other definitions for protrude that I've seen before include "Bulge" , "Stick out, project from a surface" , "Jut out" , "Stand out" , "Get through" .)