Very delayed after island gets cut off (7)
I believe the answer is:
isolate
'cut off' is the definition.
(both can mean to separate from others)
'very delayed after island' is the wordplay.
'very' becomes 'so' (both can mean 'extremely').
'delayed' becomes 'late' (running late).
'after' says to put letters next to each other.
'island' becomes 'i' (geographical abbreviation).
'so'+'late'='solate'
'solate' put after 'i' is 'ISOLATE'.
'gets' is the link.
(Other definitions for isolate that I've seen before include "Detach" , "divorce" , "Segregate. close off" , "Cut off from all contact" , "split up" .)