Rows in southern river, showing determination (10)
I believe the answer is:
steeliness
'determination' is the definition.
(I have seen 'cold determination' mean 'steeliness' so perhaps 'determination' could also mean 'steeliness')
'rows in southern river' is the wordplay.
'rows' becomes 'lines'.
'in' is an insertion indicator.
'southern' becomes 's' (abbreviation).
'river' becomes 'tees' (River Tees**).
's'+'tees'='stees'
'lines' placed within 'stees' is 'STEELINESS'.
'showing' is the link.
(Other definitions for steeliness that I've seen before include "Trustworthy condition" , "Firm determination" , "Hard nature" , "cold determination" .)