Encourage to breathe (7)
I believe the answer is:
inspire
I believe this clue is a double definition.
'encourage' is the first definition.
(inspiring is a kind of encouraging)
'breathe' is the second definition.
(I've seen this before)
'to' is the link.
(Other definitions for inspire that I've seen before include "Galvanize" , "Breathe - fire" , "Animate (with feeling)" , "Fill with ideas, enthusiasm" , "Cause to occur; animate" .)