Characteristic of monk to start to swim in northern river (7)
I believe the answer is:
tonsure
'characteristic of monk' is the definition.
(shaved part of a monk's head)
'to start to swim in northern river' is the wordplay.
'start to' says to take the initial letters.
'in' indicates putting letters inside.
'northern' becomes 'n' (abbreviation e.g. N. Ireland).
'river' becomes 'ure' (I have seen 'River of Wensleydale ' mean 'ure' so perhaps 'river' could also mean 'ure'**).
The initial letter of 'swim' is 's'.
'n'+'ure'='nure'
's' inserted into 'nure' is 'nsure'.
'to'+'nsure'='TONSURE'
(Other definitions for tonsure that I've seen before include "Result of shaving" , "Shaven area on monk's head" , "Shaven part of monk's head" , "Monk's haircut" , "Monk's hairdo" .)