Project finished, needing change in the middle (8)
I believe the answer is:
overhang
'project' is the definition.
(overhanging is a kind of projecting)
'finished needing change in the middle' is the wordplay.
'finished' becomes 'over' ('over' can be similar in meaning to 'finished').
'needing' says to put letters next to each other.
'in the middle' indicates the central letters.
The centre of 'change' is 'hang'.
'over'+'hang'='OVERHANG'
(Other definitions for overhang that I've seen before include "Beetle, lean out beyond" , "Loom above" , "Projecting part" , "Lean out beyond the vertical" , "Lean out - project" .)