Track taking dog across river (5)
I believe the answer is:
trail
'track' is the definition.
(synonyms)
'dog across river' is the wordplay.
'dog' becomes 'tail' (synonyms).
'across' is an insertion indicator.
'river' becomes 'r'.
'tail' enclosing 'r' is 'TRAIL'.
'taking' acts as a link.
(Other definitions for trail that I've seen before include "Track made through wild country" , "Rural footpath" , "Scent or track followed in hunting" , "Country path; follow" , "Be losing; track" .)