Secretary turned up with little eagerness (8)
I believe the answer is:
appetite
'eagerness' is the definition.
(thesaurus)
'secretary turned up with little' is the wordplay.
'secretary' becomes 'pa' (I've seen this in other clues).
'turned up' says the letters should be written backwards.
'with' says to put letters next to each other.
'little' becomes 'petite' ('petite' can be similar in meaning to 'little'**).
'pa' written backwards gives 'ap'.
'ap'+'petite'='APPETITE'
(Other definitions for appetite that I've seen before include "'Strong desire, craving (8)'" , "Natural desire to satisfy a need" , "stomach" , "demand" , "Physical desire as for food" .)