Acknowledge offers regularly accepted by right-wing politicians (7)
I believe the answer is:
confess
'acknowledge' is the definition.
(I know that confess is a kind of acknowledge)
'offers regularly accepted by right-wing politicians' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'accepted by' is an insertion indicator (inserted letters are accepted).
'right-wing politicians' becomes 'cons' (short for Conservatives. I am not sure about the 'right-wing' bit.).
The alternating letters of 'offers' are 'fes'.
'fes' going inside 'cons' is 'CONFESS'.
Can you help me to learn more?
(Other definitions for confess that I've seen before include "Admit (to crime)" , "Admit (to wrongdoing)" , "Tell a priest one's sins" , "Plead guilty (in order to receive absolution?)" , "Concede" .)