Holding a number on the river (6)
I believe the answer is:
tenure
'holding' is the definition.
(I've seen this in another clue)
'a number on the river' is the wordplay.
'a number' becomes 'ten' (ten is a number).
'on' means one lot of letters go next to another (in a down clue, letters appear on others).
'the river' becomes 'ure' (River Ure).
'ten'+'ure'='TENURE'
(Other definitions for tenure that I've seen before include "Length of time a position is held" , "(Right of) occupancy" , "Period holding office" , "Tenancy" , "Period of occupation" .)