Name big cat south of a northern state (8)
I believe the answer is:
announce
'state' is the definition.
(announcing is a kind of stating)
'name big cat south of a northern' is the wordplay.
'name' becomes 'n' (common abbreviation e.g. on forms).
'big cat' becomes 'ounce' (ounce is a kind of big cat).
'south of' is a charade indicator (letters next to each other) (in a down clue, some letters go under others).
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'n'+'ounce'='nounce'
'a'+'n'='an'
'nounce' after 'an' is 'ANNOUNCE'.
(Other definitions for announce that I've seen before include "Broadcast (information)" , "Make known, declare" , "Give public notice to" , "Make known publicly with no nuance" , "Make known publicly or to an audience" .)