Offering that is pounced on by the media (7)
I believe the answer is:
pressie
'offering' is the definition.
(a present is an offering)
'that is pounced on by the media' is the wordplay.
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'pounced on by' says to put letters next to each other (in a down clue, some letters go on top of others).
'the media' becomes 'press' (the press is part of the media).
'ie' put after 'press' is 'PRESSIE'.
(Other definitions for pressie that I've seen before include "Informally, offering" , "Something freely given" , "Gift (colloq.)" .)