Peter Parker ultimately being more cautious (5)
I believe the answer is:
safer
'more cautious' is the definition.
(I've seen this in another clue)
'peter parker ultimately' is the wordplay.
'peter' becomes 'safe' (slang term).
'ultimately' says to take the final letters.
The final letter of 'parker' is 'r'.
'safe'+'r'='SAFER'
'being' acts as a link.
(Other definitions for safer that I've seen before include "Less hazardous" , "Less risky" , "Less dangerous" , "Not so hairy" , "Fears (anag)" .)