Goes out seeing poor babe's missing area (4)
I believe the answer is:
ebbs
'goes out' is the definition.
'poor babe's missing area' is the wordplay.
'poor' indicates an anagram.
'missing' indicates named letters should be taken away.
'area' becomes 'a' (maths abbreviation).
'babes' with 'a' taken away is 'bbes'.
'bbes' anagrammed gives 'EBBS'.
'seeing' is the link.
(Other definitions for ebbs that I've seen before include "Goes out like tide" , "fades away" , "Flows back - declines" , "flags" , "Wanes" .)