Clue: Trump's British counterpart's the woman for you — an old nag! (7)
Answer: SHERGAR
Explanation: Definition: an old nag
SUGAR (Alan Sugar and Donald Trump appeared in the UK and US versions of *The Apprentice*) with U ("you") replaced by HER ("that woman's") – I nearly had to give up on this as I was trying to use "that woman" = SHE…