Second refill -- don't go to bed yet! (4,2)
I believe the answer is:
stop up
'don't go to bed yet' is the definition.
(to stop up is to stay up late)
'second refill' is the wordplay.
'second' becomes 's' (common abbreviation).
'refill' becomes 'top up' (I've seen this in another clue).
's'+'topup'='STOP UP'
(Other definitions for stop up that I've seen before include "Don't retire here" , "close" , "Don't go to bed early" , "Cork" , "Block (eg an earth)" .)