Seventh of connections Everyman is going to cultivate (4)
I believe the answer is:
till
'cultivate' is the definition.
(I've seen this before)
'seventh of connections everyman is going to' is the wordplay.
'seventh of connections' becomes 't' (7th letter of 'connections').
'everyman is going to' becomes 'I'll' (where 'Everyman' is the setter of the crossword).
't'+'ill'='TILL'
(Other definitions for till that I've seen before include "Checkout - cultivate (land)" , "Drawer holding money in shop." , "Up to (a point in time)" , "not starting yet" , "Small box in shop for holding cash" .)