Claim to offer a type of media coverage (7)
I believe the answer is:
profess
'claim' is the definition.
(I know that profess is a more specific form of the action claim)
'of media coverage' is the wordplay.
'media' becomes 'press' (the press is part of the media).
'coverage' indicates putting letters inside.
'of' put inside 'press' is 'PROFESS'.
'to offer a type' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for profess that I've seen before include "Claim or declare" , "Affirm faith in (religion)" , "State insincerely" , "Make open declaration of" , "Declare openly" .)