Keep on being saucy about half-sister (7)
I believe the answer is:
persist
'keep on' is the definition.
(thesaurus)
'saucy about half-sister' is the wordplay.
'saucy' becomes 'pert' ('pert' can be a synonym of 'saucy').
'about' indicates putting letters inside.
'half' means to take half the letters.
'sister' with half the letters taken is 'sis'.
'pert' going around 'sis' is 'PERSIST'.
'being' is the link.
(Other definitions for persist that I've seen before include "Continue (in spite of difficulties)" , "Show doggedness" , "Continue to exist" , "Continue in spite of difficulty" , "Stripes (anag)" .)