After reshuffle, Attlee ran for deputy (9)
I believe the answer is:
alternate
'deputy' is the definition.
(I've seen this before)
'after reshuffle attlee ran' is the wordplay.
'after reshuffle' indicates an anagram (letters shuffled around).
'attlee'+'ran'='attleeran'
'attleeran' is an anagram of 'ALTERNATE'.
'for' acts as a link.
(Other definitions for alternate that I've seen before include "Change repeatedly between two" , "Every second one of a series" , "Change from one thing to another by turns" , "Occurring in turn repeatedly" , "Substitute" .)