Greek character’s record on pit administration ultimately (7)
I believe the answer is:
epsilon
'greek character's' is the definition.
(letter from the Greek alphabet)
'record on pit administration ultimately' is the wordplay.
'record' becomes 'EP' (abbreviation for extended play record).
'on pit' becomes 'silo' (I can't justify this - if you can you should give a lot more credence to this answer).
'ultimately' suggests the final letters.
The final letter of 'administration' is 'n'.
'ep'+'silo'+'n'='EPSILON'
Can you help me to learn more?
(Other definitions for epsilon that I've seen before include "Greek short E" , "small number mispronounced, almost completely the wrong way round" , "character in Greece" , "Greek letter - pinoles (anag)" , "foreign letter" .)