A little bit of information shortly turning up (3)
I believe the answer is:
tad
'a little bit' is the definition.
(a tad means a little)
'information shortly turning up' is the wordplay.
'information' becomes 'data' (data are bits of information).
'shortly' means to remove the last letter.
'turning up' is a reversal indicator.
'data' with its last letter removed is 'dat'.
'dat' backwards is 'TAD'.
'of' is the link.
(Other definitions for tad that I've seen before include "Modest amount" , "little boy" , "Small amount or degree" , "Small bit" , "(A) bit, touch" .)