Precious little, the time before (4)
I believe the answer is:
twee
'precious' is the definition.
(I've seen this before)
'little the time before' is the wordplay.
'little' becomes 'wee' (similar in meaning).
'the time' becomes 't' (abbreviation).
'before' means one lot of letters go next to another.
'wee' after 't' is 'TWEE'.
(Other definitions for twee that I've seen before include "Affectedly pretty" , "Affected quaint" , "Sentimental, quaint" , "rather quaint" , "Affectedly sweet" .)