Precious time? Minute, perhaps (4)
I believe the answer is:
twee
'precious' is the definition.
(I've seen this before)
'time minute perhaps' is the wordplay.
'time' becomes 't' (abbreviation).
'minute perhaps' becomes 'wee' (wee can mean very small).
't'+'wee'='TWEE'
(Other definitions for twee that I've seen before include "Sentimentally pretty" , "Overly sentimental or pretty" , "Excessively quaint" , "Small and pretty" , "Mawkish" .)