The don is tired of covering for self-indulgent person (8)
I believe the answer is:
hedonist
'self-indulgent person' is the definition.
'hedonist' can be an answer for 'person' (hedonist is a kind of person). I'm unsure of the 'self-indulgent' bit.
'the don is tired of covering' is the wordplay.
'covering' indicates the answer is hidden within the clue.
'HEDONIST' is hidden within 'the don is tired of'.
'for' acts as a link.
Can you help me to learn more?
(Other definitions for hedonist that I've seen before include "One who lives only for pleasure" , "A seeker after luxury" , "he puts pleasure before work" , "playboy" , "Extreme pleasure-seeker" .)