Admits, sadly, to getting into the centre of it (6)
I believe the answer is:
amidst
'getting into the centre of it' is the definition.
I don't know anything about this answer so I can't judge whether this works.
'admits sadly' is the wordplay.
'sadly' indicates an anagram.
'admits' anagrammed gives 'AMIDST'.
'to' acts as a link.
Can you help me to learn more?
(Other definitions for amidst that I've seen before include "Central" , "In the thick of" , "It's mad (anag.)" , "Admits (anag.)" , "Among" .)