An assignment in ones palmy days? (4)
I believe the answer is:
date
'an assignment' is the definition.
Although both the answer and definition are singular nouns, I don't see how they can define each other.
'ones palmy days?' is the wordplay.
I cannot really understand how this works, but
'days?' could be 'd' (abbreviation for days) and 'd' is present in the answer.
The remaining letters 'ate' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'in' acts as a link.
Can you help me to learn more?
(Other definitions for date that I've seen before include "Step out with" , "Sweet edible fruit" , "See 12" , "Particular time of event - fruit" , "Estimate age of" .)