Regularly connected previously (4)
I believe the answer is:
once
'previously' is the definition.
(once means in the past)
'regularly connected' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
The alternate letters of 'connected' are 'ONCE'.
(Other definitions for once that I've seen before include "At some time past" , "not repeatedly" , "Formerly; as soon as" , "In the old days" , "in bygone era" .)