Gives up when a spider's revealed (8)
I believe the answer is:
despairs
'gives up' is the definition.
(I've seen this in another clue)
'a spider's revealed' is the wordplay.
'revealed' is an anagram indicator.
'a'+'spiders'='aspiders'
'aspiders' is an anagram of 'DESPAIRS'.
'when' is the link.
(Other definitions for despairs that I've seen before include "Abandons hope" , "Loses all hope" .)