Getting to the end of this exhausts one's patience (6)
I believe the answer is:
tether
'end of this exhausts one's patience' is the definition.
The definition suggests a singular noun which matches the answer.
'getting to the' is the wordplay.
I cannot quite see how this works, but
an anagram of 'the' is 'eth' which is present in the answer.
This may be the basis of clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for tether that I've seen before include "Tie up with a rope, an animal perhaps" , "lead" , "Rope for confining animal" , "restrain boxers, say" , "Restraint for animal" .)