Smile having caught river fish (5)
I believe the answer is:
bream
'fish' is the definition.
(type of fish)
'smile having caught river' is the wordplay.
'smile' becomes 'beam' (to beam is to smile).
'having caught' is an insertion indicator.
'river' becomes 'r' (abbreviation for river).
'beam' going around 'r' is 'BREAM'.
(Other definitions for bream that I've seen before include "Fish - British classical guitarist, b. 1933" , "Fish - English guitarist" , "Amber (anag) - fish" , "Carp relative" , "River fish" .)