Endure nasty virus very close to home (7)
I believe the answer is:
'endure' is the definition.
('survive' can be a synonym of 'endure')
'nasty virus very close to home' is the wordplay.
'nasty' indicates anagramming the letters.
'very' becomes 'v' (abbreviation).
'close to' suggests the final letters (the close/ending of).
The final letter of 'home' is 'e'.
'virus' anagrammed gives 'survi'.
(Other definitions for survive that I've seen before include "Continue to exist", "Live on", "Continue living", "Outlast", "Remain alive".)