Alien getting unwrapped suit into case (4)
I believe the answer is:
etui
'case' is the definition.
(case for needlework equipment)
'alien getting unwrapped suit' is the wordplay.
'alien' becomes 'et' (extra terrestrial).
'getting' means one lot of letters go next to another.
'unwrapped' means to look at the middle letters (the letters which wrap the word are removed).
The centre of 'suit' is 'ui'.
'et'+'ui'='ETUI'
'into' acts as a link.
(Other definitions for etui that I've seen before include "a seamstress requires?" , "Small case for small things" , "Small needle case e" , "Ornamental bag for needles etc." , "Needlework case" .)