Clothing caught by épée awfully near point (7)
I believe the answer is:
perigee
'near point' is the definition.
(astronomical term)
'clothing caught by epee awfully' is the wordplay.
'clothing' becomes 'rig' (rig is a kind of clothing).
'caught by' means one lot of letters goes inside another.
'awfully' is an anagram indicator.
'epee' is an anagram of 'peee'.
'rig' placed inside 'peee' is 'PERIGEE'.
(Other definitions for perigee that I've seen before include "Point of orbit closest to the earth" , "where orbit's lowest" , "Lowest orbit point" , "A low point" , "Point of orbit nearest earth" .)