Duke terribly late finds river mouth (5)
I believe the answer is:
delta
'river mouth' is the definition.
(I've seen this before)
'duke terribly late' is the wordplay.
'duke' becomes 'd' (abbreviation).
'terribly' indicates an anagram.
'late' is an anagram of 'elta'.
'd'+'elta'='DELTA'
'finds' acts as a link.
(Other definitions for delta that I've seen before include "Wide silted river mouth" , "Branching river mouth" , "Greek character" , "Nile river mouth" , "Fourth letter of the ancient Greek alphabet: river feature" .)