Fantastic sight after European husband climbs summits (7)
I believe the answer is:
heights
'summits' is the definition.
('height' can be a synonym of 'summit')
'fantastic sight after european husband climbs' is the wordplay.
'fantastic' is an anagram indicator (a fantastic or improbable ordering of the letters).
'after' says to put letters next to each other.
'european' becomes 'e' (abbreviation e.g. EU).
'husband' becomes 'h' (abbreviation).
'climbs' shows that the letters should be reversed in order.
'e'+'h'='eh'
'eh' written backwards gives 'he'.
'sight' anagrammed gives 'ights'.
'ights' put after 'he' is 'HEIGHTS'.
(Other definitions for heights that I've seen before include "'Altitudes, elevations (7)'" , "Hills, elevated places" , "Peaks" , "See 10" , "High places" .)