Difficult politician left former partner's business at the outset (7)
I believe the answer is:
complex
'difficult' is the definition.
(I've seen this before)
'politician left former partner's business at the outset' is the wordplay.
'politician' becomes 'MP' (Member of Parliament).
'left' becomes 'l' (common abbreviation).
'former partner' becomes 'ex' (an ex-partner).
'business' becomes 'co' (short for company).
'at the outset' is a charade indicator (letters next to each other).
'mp'+'l'+'ex'='mplex'
'mplex' put after 'co' is 'COMPLEX'.
(Other definitions for complex that I've seen before include "'Complicated, intricate (7)'" , "Preoccupation" , "Consisting of interconnected parts" , "with real and imaginary parts" , "Convoluted" .)