Hope last seen of apparent decay (5)
I believe the answer is:
trust
'hope' is the definition.
('trust' can be a synonym of 'hope')
'last seen of apparent decay' is the wordplay.
'last seen of' suggests the final letters.
'decay' becomes 'rust' (rusting is a kind of decaying**).
The last letter of 'apparent' is 't'.
't'+'rust'='TRUST'
(Other definitions for trust that I've seen before include "assurance" , "Firm belief (in someone/something)" , "Firm belief (in someone)" , "Have faith or confidence in reliability of" , "Have faith in, regard as reliable" .)