Something that obstructs black bird, cutting head (7)
I believe the answer is:
barrier
'something' is the definition.
(I know that barrier is a type of something)
'obstructs black bird cutting head' is the wordplay.
'obstructs black' becomes 'bar' (I am not sure about this - if you are sure you should believe this answer much more).
'bird' becomes 'frier' (frier is a kind of bird).
'cutting head' means to remove the first letter.
'frier' with its initial letter taken away is 'rier'.
'bar'+'rier'='BARRIER'
'that' is the link.
Can you help me to learn more?
(Other definitions for barrier that I've seen before include "It impedes free movement" , "Obstacle to movement" , "Thing preventing passage or access" , "fencing?" , "Rear rib may present obstacle" .)