Fruit that's old and turning bad (5)
I believe the answer is:
olive
'fruit' is the definition.
(I've seen this before)
'old and turning bad' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'and' says to put letters next to each other.
'turning' says the letters should be written backwards.
'bad' becomes 'evil' ('evil' is associated in meaning with 'bad').
'evil' written backwards gives 'live'.
'o'+'live'='OLIVE'
'that's' acts as a link.
(Other definitions for olive that I've seen before include "shades of green" , "Girl's name - colour" , "Mediterranean fruit or greenish colour" , "woman" , "Girl's name; tree" .)