Survive since no one uses the exit later (7)
I believe the answer is:
outlast
'survive' is the definition.
(I know that survive can be written as outlast)
'no one uses the exit later' is the wordplay.
'no' becomes 'O' (O resembles 0).
'one uses the exit' becomes 'ut' (I can't justify this - if you can you should give a lot more credence to this answer).
'later' becomes 'last' (synonyms).
'o'+'ut'+'last'='OUTLAST'
'since' acts as a link.
This may not be right. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for outlast that I've seen before include "Live longer than" , "Lout sat (anag.)" , "Persist longer than" , "carry on after all others" , "Survive beyond" .)