Again having got across (4)
I believe the answer is:
over
This might be a double definition.
'again' is the first definition.
(as in the phrases 'start over' and 'start again')
'across' is the second definition.
(synonyms)
'having got' acts as a link.
I am not very happy about this link. Some or all of it may belong to one of the definitions.
Can you help me to learn more?
(Other definitions for over that I've seen before include "settled" , "Rouond of six bowls in cricket" , "Finished -- as a remainder" , "Six cricket deliveries" , "bridge?" .)