Just a little short of up to date (3)
I believe the answer is:
tad
'just a little short' is the definition.
I can't tell whether this defines the answer.
'up to date' is the wordplay.
'up to' becomes 'ta' (I can't explain this - if you can you should believe this answer much more).
'date' becomes 'd' (common abbreviation eg in DOB, date of birth).
'ta'+'d'='TAD'
'of' acts as a link.
Can you help me to learn more?
(Other definitions for tad that I've seen before include "(A) bit, touch" , "A small amount (colloq.)" , "Smidgen" , "Modest amount" , "little boy" .)