Bit of time after date ... (3)
I believe the answer is:
tad
'bit' is the definition.
(I've seen this before)
'time after date' is the wordplay.
'time' becomes 't'.
'after' says to put letters next to each other.
'date' becomes 'ad' (AD is an example).
't'+'ad'='TAD'
'of' acts as a link.
(Other definitions for tad that I've seen before include "Small amount or degree" , "Slight amount" , "Small bit" , "Modest amount" , "little boy" .)