Egg on guy initially entering Yorkshire river (4)
I believe the answer is:
urge
'egg on' is the definition.
(to egg on is to urge or encourage)
'guy initially entering yorkshire river' is the wordplay.
'initially' says to take the initial letters.
'entering' means one lot of letters goes inside another.
'yorkshire river' becomes 'ure' (River Ure).
The first letter of 'guy' is 'g'.
'g' placed within 'ure' is 'URGE'.
(Other definitions for urge that I've seen before include "Advise strongly or prod" , "Itch" , "Incite to action" , "Strongly recommend; impulse" , "Sudden desire" .)