Famous Indian. Run out he comes back in (5)
I believe the answer is:
nehru
'famous indian' is the definition.
(I've seen this before)
'run out he comes back in' is the wordplay.
'out' indicates an anagram (out can mean wrong or inaccurate).
'comes back' says the letters should be written backwards.
'in' means one lot of letters goes inside another.
'he' in reverse letter order is 'eh'.
'run' is an anagram of 'nru'.
'nru' going around 'eh' is 'NEHRU'.
(Other definitions for nehru that I've seen before include "First Indian prime minister, 1947-64" , "First prime minister of India" , "former statesman" , "Student of Gandhi" , "Former Indian PM" .)