Characteristic of extremely scary animals essentially is to chase soft cat (7)
I believe the answer is:
symptom
'characteristic' is the definition.
(thesaurus)
'extremely scary animals essentially is to chase soft cat' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'essentially' indicates the central letters.
'is to chase' is a charade indicator (letters next to each other).
'soft' becomes 'p' (musical abbreviation for 'piano').
'cat' becomes 'tom' (a tom is a male cat).
'scary' with its centre removed is 'sy'.
The centre of 'animals' is 'm'.
'sy'+'m'+'p'+'tom'='SYMPTOM'
'of' is the link.
(Other definitions for symptom that I've seen before include "It indicates disease" , "Indication (of disease, problem)" , "Sign of disease" , "Sign; indication" , "sign all's not well" .)