My parking space rather confined (4)
I believe the answer is:
coop
'space rather confined' is the definition.
'my parking' is the wordplay.
'my' becomes 'coo' (I've seen this before**).
'parking' becomes 'p'.
'coo'+'p'='COOP'
(Other definitions for coop that I've seen before include "Hens in this" , "Pen" , "pound" , "Birdcage" , "Cage for poultry" .)