A lot refuse to admit it's on the way up (7)
I believe the answer is:
destiny
'a lot' is the definition.
(lot as in a person's luck)
'refuse to admit it's on the way up' is the wordplay.
'refuse' becomes 'deny' ('deny' can be a synonym of 'refuse'**).
'to admit' is an insertion indicator.
'on the way up' is a reversal indicator.
'its' backwards is 'sti'.
'deny' going around 'sti' is 'DESTINY'.
(Other definitions for destiny that I've seen before include "The future as arranged by fate" , "portion" , "Fortune" , "Lot" , "Kismet, fate" .)