Past prime minister with her unfashionable jacket (5)
I believe the answer is:
nehru
'past prime minister' is the definition.
(former Indian prime minister Jawaharlal Nehru)
'her unfashionable jacket' is the wordplay.
I cannot really understand how this works, but
an anagram of 'her' is 'ehr' which is within the answer.
The remaining letters 'nu' is a valid word which might be clued in a way I don't see.
This may be the basis of clue (or it may be nonsense).
'with' is the link.
(Other definitions for nehru that I've seen before include "Popular Indian" , "India's first prime minister" , "First Indian prime minister, 1947-64" , "Former Indian PM" , "Indian statesman" .)