Has obligation, being hunted to hide head (5)
I believe the answer is:
ought
'has obligation' is the definition.
(someone who ought to do something is obliged)
'hunted to hide head' is the wordplay.
'hunted' becomes 'sought'.
'to hide head' means to remove the first letter.
'sought' with its first letter taken away is 'OUGHT'.
'being' acts as a link.
(Other definitions for ought that I've seen before include "Strange thing" , "Be bound" , "Anything at all (archaic)" , "Have/has a duty (to do)" , "Has a duty (to do something)" .)