Every second, a flier's coming in behind schedule (9)
I believe the answer is:
Here is my best explanation:
'every second' is the definition.
('alternate' can be a synonym of 'every second')
'a flier's coming in behind schedule' is the subsidiary indication.
'flier' becomes 'tern' (tern is a kind of birdanimal**).
'coming in' means one lot of letters goes inside another.
'behind schedule' becomes 'late' (I've seen this in other clues).
'tern' inserted inside 'late' is 'lternate'.
(Other definitions for alternate that I've seen before include "Do in turn repeatedly", "substitute", "Happen in turns, rotate", "Occur in turn repeatedly", "Change from one thing to another by turns", "go back and forth", "By turns, first one then the other", "Go in turns", "Every second one of a series" and "Interchange".)