Stadium lacking in new locality (4)
I believe the answer is:
area
'locality' is the definition.
(I've seen this before)
'stadium lacking in new' is the wordplay.
'stadium' becomes 'arean' (I've seen this before).
'lacking in' suggests deleting specific letters.
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'arean' with 'n' removed is 'AREA'.
(Other definitions for area that I've seen before include "environs" , "Field of activity or surface" , "The measure of a surface" , "Surface measurement" , "Extent of a two-dimensional surface" .)