It flies Times into oil well at sea (6,3)
I believe the answer is:
little owl
'it flies' is the definition.
(bird which flies)
'times into oil well at sea' is the wordplay.
'times' becomes 'tt' (two abbreviations for time).
'into' is an insertion indicator.
'at sea' indicates an anagram.
'oil'+'well'='oilwell'
'oilwell' is an anagram of 'lileowl'.
'tt' put inside 'lileowl' is 'LITTLE OWL'.
(Other definitions for little owl that I've seen before include "Small bird of prey" , "Flyer" , "flier" , "inappropriate for this bird" .)