It symbolises rebirth of hope in troubled times (7)
I believe the answer is:
phoenix
'it symbolises rebirth' is the definition.
'hope in troubled times' is the wordplay.
'troubled' indicates an anagram.
'times' becomes 'x' (multiplication sign).
'hope'+'in'='hopein'
'hopein' is an anagram of 'phoeni'.
'phoeni'+'x'='PHOENIX'
'of' is the link.
(Other definitions for phoenix that I've seen before include "Reborn bird" , "Legendary bird born from ashes" , "Legendary bird said to emerge from the ashes of itself" , "Mythical bird rising from funeral pyre" , "Legendary bird -- Arizona city" .)