River discovered by Rex, camping? (5)
I believe the answer is:
'river' is the definition.
'by rex camping?' is the wordplay.
I cannot really see how this works, but
'rex' could be 'r' (common abbreviation e.g. GR=George Rex, King Georg) and 'r' is found in the answer.
'camping?' could be 'tent' (I've seen this in other clues) and 'tent' is located in the remaining letters.
This accounts for all the letters.
This explanation may well be incorrect...
'discovered' acts as a link.
(Other definitions for trent that I've seen before include "Nottingham's river", "Burton's river", "Stoke's river", "Eng. river; Council of -", "Chief river of the Midlands".)