Connected periodically in the past (4)
I believe the answer is:
once
'in the past' is the definition.
(once upon a time)
'connected periodically' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
The alternate letters of 'connected' are 'ONCE'.
(Other definitions for once that I've seen before include "Just as a single occurrence" , "not repeatedly" , "Formerly; as soon as" , "Quick examination" , "In times past" .)