Determined little girl, ten, saucy on the outside (10)
I believe the answer is:
persistent
'determined' is the definition.
(thesaurus)
'little girl ten saucy on the outside' is the wordplay.
'little girl' becomes 'sis' (I've seen this in other clues).
'saucy' becomes 'pert' ('pert' can be a synonym of 'saucy').
'on the outside' means one lot of letters goes inside another.
'sis'+'ten'='sisten'
'sisten' inserted into 'pert' is 'PERSISTENT'.
(Other definitions for persistent that I've seen before include "single-minded" , "Ongoing" , "Relentless" , "Not taking "no" for an answer" , "Prolonged; nagging" .)