I go out with inspiring European, and conceive (6)
I believe the answer is:
ideate
'conceive' is the definition.
(synonyms)
'i go out with inspiring european' is the wordplay.
'go out with' becomes 'date' (synonyms).
'inspiring' indicates putting letters inside.
'european' becomes 'E' (abbreviation e.g. EU).
'date' going around 'e' is 'deate'.
'i'+'deate'='IDEATE'
'and' acts as a link.
(Other definitions for ideate that I've seen before include "Form in the imagination" , "Imagine (psychology), aid tee (anag.)" , "Fancy" , "Form a picture of" .)