After being connected – oddly disappearing (4)
I believe the answer is:
once
'after' is the definition.
(once can mean immediately after)
'connected oddly disappearing' is the wordplay.
'oddly disappearing' means one should take alternating letters (letters in odd-numbered positions removed).
The alternate letters of 'connected' are 'ONCE'.
'being' is the link.
(Other definitions for once that I've seen before include "In days past" , "'... bitten, twice shy'" , "One-time musical film and song" , "Quick examination" , "not repeatedly" .)