Tight old solver's admitting disagreement (7)
I believe the answer is:
thrifty
'tight' is the definition.
(both can mean reluctant to spend money)
'old solver's admitting disagreement' is the wordplay.
'old solver's' becomes 'thy' (belonging to thee, the crossword solver).
'admitting' means one lot of letters goes inside another (admit can mean to welcome in or accept).
'disagreement' becomes 'rift' (I've seen this in another clue).
'thy' going around 'rift' is 'THRIFTY'.
(Other definitions for thrifty that I've seen before include "Not extravagant" , "Careful and diligent in the use of resources" , "Careful with money" , "Sparing" , "Frugal - economical" .)