Set about crossing European river (4)
I believe the answer is:
tees
'river' is the definition.
(River Tees )
'set about crossing european' is the wordplay.
'about' is a reversal indicator.
'crossing' indicates putting letters inside (to cross can mean to go over or around).
'european' becomes 'E' (abbreviation e.g. EU).
'set' in reverse letter order is 'tes'.
'tes' going around 'e' is 'TEES'.
(Other definitions for tees that I've seen before include "Golfer's supports; river" , "Stockton's river" , "Durham's river" , "Northern river" , "Current" .)