Complete closure of precinct, including record store (5)
I believe the answer is:
depot
'store' is the definition.
(depot can mean a store or warehouse)
'complete closure of precinct including record' is the wordplay.
'complete' becomes 'do' (doing is a kind of completing).
'closure of' suggests the final letters.
'including' indicates putting letters inside.
'record' becomes 'EP' (abbreviation for extended play record).
The final letter of 'precinct' is 't'.
'do'+'t'='dot'
'dot' going around 'ep' is 'DEPOT'.
(Other definitions for depot that I've seen before include "Supply base" , "(Military) store" , "Large storage site" , "Regimental HQ" , "Toped (anag.)" .)