Being thrifty using mat found in river (6)
I believe the answer is:
frugal
'being thrifty' is the definition.
('frugal' can be similar in meaning to 'thrifty')
'mat found in river' is the wordplay.
'mat' becomes 'rug' (I've seen this before).
'found in' means one lot of letters goes inside another.
'river' becomes 'fal' (I've seen this before**).
'rug' put into 'fal' is 'FRUGAL'.
'using' acts as a link.
(Other definitions for frugal that I've seen before include "Thrifty or parsimonious" , "Sparing, meagre" , "Abstemious" , "Not wanting waste" , "Sparing with resources" .)