Strict rule: radio has to impress Yankee (7)
I believe the answer is:
tyranny
'strict rule' is the definition.
(a tyrant rules strictly or severely)
'radio has to impress yankee' is the wordplay.
'radio' becomes 'tranny' (short for transistor radio).
'has to impress' means one lot of letters goes inside another (inserted letters are pressed inside).
'yankee' becomes 'Y' (phonetic alphabet: alpha, bravo, charlie etc.).
'tranny' going around 'y' is 'TYRANNY'.
(Other definitions for tyranny that I've seen before include "Cruel rulers" , "Despotic rule" , "Cruel government" , "Excessive use of power" , "Form of despotism" .)