Old lodger rejecting a new amount (6)
I believe the answer is:
extent
'new amount' is the definition.
'extent' can be an answer for 'amount' (thesaurus). I'm not certain of the 'new' bit.
'old lodger rejecting a' is the wordplay.
'old' becomes 'ex' (prefix meaning former or onetime).
'lodger' becomes 'tenant' (I've seen this in another clue).
'rejecting' indicates named letters should be taken away.
'a' becomes 'an'.
'tenant' with 'an' taken out is 'tent'.
'ex'+'tent'='EXTENT'
(Other definitions for extent that I've seen before include "Area; size" , "Degree - amount - scope" , "Area something covers" , "Length" , "Area covered by something" .)