Sent out to wrap Ellie's first present, perhaps? (5)
I believe the answer is:
tense
'present perhaps?' is the definition.
(present is a kind of tense)
'sent out to wrap ellie's first' is the wordplay.
'out' is an anagram indicator (out can mean wrong or inaccurate).
'to wrap' indicates putting letters inside.
'first' indicates taking the first letters.
The initial letter of 'ellie' is 'e'.
'sent' anagrammed gives 'tnse'.
'tnse' placed around 'e' is 'TENSE'.
(Other definitions for tense that I've seen before include "perfect, perhaps" , "past possibly" , "Anxious - future, perhaps?" , "not together?" , "In a nervous state" .)