Restrained a tendency to eat eggs up (9)
I believe the answer is:
abstinent
'restrained' is the definition.
(I've seen this before)
'a tendency to eat eggs up' is the wordplay.
'tendency' becomes 'bent' (bent can mean a propensity or tendency).
'to eat' means one lot of letters goes inside another.
'eggs' becomes 'nits' (nits are insect eggs).
'up' is a reversal indicator (in down clue: letters go upwards).
'nits' reversed gives 'stin'.
'bent' going around 'stin' is 'bstinent'.
'a'+'bstinent'='ABSTINENT'
(Other definitions for abstinent that I've seen before include "On the wagon" , "self-restraint" , "Avoiding alcohol" , "without booze" , "Going without, especially food and alcohol" .)