Fatigued by the rough ride on Tuesday (5)
I believe the answer is:
tired
'fatigued' is the definition.
('tire' can be a synonym of 'fatigue')
'the rough ride on tuesday' is the wordplay.
'the rough' indicates an anagram (a rough or broken ordering of the letters).
'on' is a charade indicator (letters next to each other).
'tuesday' becomes 't' ().
'ride' anagrammed gives 'ired'.
'ired' after 't' is 'TIRED'.
'by' acts as a link.
(Other definitions for tired that I've seen before include "Sleepy" , "getting bored" , "Whacked" , "Beat" , "Worn out" .)