Spend the night - a lot of corsets dispensed with (4,4)
I believe the answer is:
stay over
'spend the night' is the definition.
(to stay over somewhere is to spend the night there)
'a lot of corsets dispensed with' is the wordplay.
'a lot of' means to remove the last letter (I've seen 'lots of' mean this (the majority of the word)).
'corsets' becomes 'stays' (I've seen this before).
'dispensed with' becomes 'over' (over can mean finished or done with).
'stays' with its last letter taken away is 'stay'.
'stay'+'over'='STAY OVER'
(Another definition for stay over that I've seen is " not to leave till morning?".)