Masses toil endlessly after his inauguration and election (3,6)
I believe the answer is:
hoi polloi
'masses' is the definition.
(Greek term for the common people)
'toil endlessly after his inauguration and election' is the wordplay.
'endlessly' means to look at the middle letters (the ends of the words are removed).
'after' says to put letters next to each other.
'his inauguration' becomes 'hoi' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'and' is a charade indicator (letters next to each other).
'election' becomes 'poll' (I've seen this before).
The centre of 'toil' is 'oi'.
'hoi'+'poll'='hoipoll'
'oi' after 'hoipoll' is 'HOI-POLLOI'.
Can you help me to learn more?
(Other definitions for hoi polloi that I've seen before include "The unwashed masses!" , "commoners" , "vulgar rabble" , "(Often derogatory) term for the masses or common people" , "Riff-raff" .)