Dominant woman, busy person chasing cat (5,3)
I believe the answer is:
queen bee
'dominant woman' is the definition.
(I've seen this before)
'busy person chasing cat' is the wordplay.
'busy person' becomes 'bee' (I've seen this in other clues).
'chasing' means one lot of letters go next to another.
'cat' becomes 'queen' (a queen is a female cat).
'bee' after 'queen' is 'QUEEN-BEE'.
(Other definitions for queen bee that I've seen before include "Important woman" , "Woman of importance" , "Dominant woman - chief buzzer?" , "Egg-laying apian sort" , "The fertile, non-working female of the hive" .)