Approaches swan swimming in bleak surroundings (5,4)
I believe the answer is:
draws near
'approaches' is the definition.
('draw near' can be a synonym of 'approach')
'swan swimming in bleak surroundings' is the wordplay.
'swimming in' indicates anagramming the letters.
'bleak' becomes 'drear' (I've seen this before).
'surroundings' is an insertion indicator.
'swan' is an anagram of 'awsn'.
'awsn' put inside 'drear' is 'DRAWS NEAR'.
(Other definitions for draws near that I've seen before include "Approaches" , "comes to" .)