Courage shown by fool crossing river (4)
I believe the answer is:
grit
'courage' is the definition.
(I've seen this before)
'fool crossing river' is the wordplay.
'fool' becomes 'git' (both can mean an annoying person).
'crossing' means one lot of letters goes inside another (to cross can mean to go over or around).
'river' becomes 'r' (abbreviation).
'git' going around 'r' is 'GRIT'.
'shown by' is the link.
(Other definitions for grit that I've seen before include "Stone particles; pluck" , "Guts and gumption" , "True determination?" , "Small hard particles - determination" , "Determination - small stones" .)