Registers open-top cars? Not these days (7)
I believe the answer is:
'registers' is the definition.
(a roster is a register or list of people)
'open-top cars? not these days' is the wordplay.
'open-top cars?' becomes 'roadsters' (a roadster is an open-top car).
'not' suggests deleting specific letters.
'these days' becomes 'AD' (as in Anno Domini, after Christ).
'roadsters' with 'ad' taken out is 'ROSTERS'.
(Another definition for rosters that I've seen is " Schedules of times to be on duty".)