Be after a familiar name for Lincoln (3)
I believe the answer is:
abe
'for lincoln' is the definition.
(I've seen this in another clue)
'be after a' is the wordplay.
'after' means one lot of letters go next to another.
'be' put after 'a' is 'ABE'.
'familiar name' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for abe that I've seen before include "Eg, president Lincoln" , "Lincoln's diminutive" , "President Lincoln was known as Honest ..." , "Lincoln, familiarly" .)