Only half sleeps in poor area (4)
I believe the answer is:
slum
'poor area' is the definition.
'only half sleeps' is the wordplay.
'only half' suggests halving the letters.
'sleeps' becomes 'slumbers' ('slumber' can be a synonym of 'sleep').
'slumbers' with half the letters taken is 'SLUM'.
'in' is the link.
(Other definitions for slum that I've seen before include "Squalid neighbourhood" , "Area of poor housing" , "Over-crowded run-down city area" , "Squalid and overcrowded urban area" , "Run-down housing area" .)