In time a natural evolution of the spider (9)
I believe the answer is:
tarantula
'spider' is the definition.
(I know that tarantula is a type of spider)
'in time a natural evolution' is the wordplay.
'in' is an insertion indicator.
'time' becomes 't' (abbreviation).
'evolution' indicates an anagram.
't'+'a'='ta'
'natural' is an anagram of 'arantul'.
'ta' going around 'arantul' is 'TARANTULA'.
'of the' acts as a link.
(Other definitions for tarantula that I've seen before include "Breed of spider" , "Crawler" , "Large venomous spider" , "web architect" , "Creepy-crawly" .)