Yet to do an upgrade to R15.3 but in my newly installed R15.3 system, with PMO installed, if I set the Activate New User Experience check box under Administration, General Settings, System Options, New User Experience section, and saved the greyed out Activate Timesheets checkbox could be updated.
Found once Activate Timesheets was set, then only TS from the New UX available and nothing from the classic. However, it the Activate Timesheets was unchecked the option was removed from the new UX and the original icons appeared.
The following SQL will show if this Option is Set (1) or not set (0) in the system
SELECT
value
FROM
CMN_OPTION_VALUES
WHERE OPTION_ID=(SELECT ID FROM CMN_OPTIONS WHERE OPTION_CODE = 'TIMESHEET_WAR_APP_ENABLED')