Old president not quite retired (3)
I believe the answer is:
abe
'old president' is the definition.
(Abraham (Abe) Lincoln)
'not quite retired' is the wordplay.
'not quite' means to remove the last letter (most but not all of the word).
'retired' becomes 'abed' (I've seen this in another clue).
'abed' with its final letter taken off is 'ABE'.
(Other definitions for abe that I've seen before include "Lincoln's diminutive" , "President Lincoln was known as Honest ..." , "Eg, president Lincoln" , "Lincoln, familiarly" .)