Projection, which could produce a headache with part exchange (8)
I believe the answer is:
overhang
'projection' is the definition.
(I know that overhang is a type of projection)
'could produce a headache with part exchange' is the wordplay.
I cannot really see how this works, but
'a' could be 'an' and 'an' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
'which' acts as a link.
(Other definitions for overhang that I've seen before include "Projecting part" , "Loom above" , "Lean out beyond the vertical" , "Beetle, lean out beyond" , "Extend beyond (a roof, perhaps)" .)