Spider starts to tremble after natural disaster (9)
I believe the answer is:
tarantula
'spider' is the definition.
(I know that tarantula is a type of wolf spider)
'starts to tremble after natural disaster' is the wordplay.
'starts to' indicates taking the first letters.
'disaster' indicates anagramming the letters.
The initial letters of 'tremble after' is 'ta'.
'natural' with letters rearranged gives 'rantula'.
'ta'+'rantula'='TARANTULA'
(Other definitions for tarantula that I've seen before include "web developer" , "small, venomous creature" , "A large hairy tropical spider" , "Crawler" , "A big hairy spider" .)