Search to capture alien life? It’s an obsession (6)
I believe the answer is:
fetish
'an obsession' is the definition.
(an obsession or fascination with something)
'search to capture alien life?' is the wordplay.
'search' becomes 'fish' (fishing is a kind of searching).
'to capture' means one lot of letters goes inside another.
'alien life?' becomes 'ET' (extraterrestrial).
'fish' enclosing 'et' is 'FETISH'.
'it's' acts as a link.
(Other definitions for fetish that I've seen before include "Object worshipped by primitive people or of abnormal sexual interest" , "magical object" , "Object worshipped as having a spirit" , "thing?" , "Object worshipped by primitive people or fixation (6)" .)