The most common and most likely answer to this crossword clue is the 6 letter word TETHER
I've seen this crossword clue in The Guardian
T
E
T
H
E
R
More clues leading to the result TETHER
- Fixer essential to renovate the room
- Tie in league, avoiding own goal
- Not all appreciate the rector’s tie
- Article secured by odd bits of their rope
- Element of vote the right must secure
- First element of telephone number provides lead
- Fasten article in short time
- Getting to the end of this exhausts one’s patience
- Restrain head of therapy with drug
- Rope carried by private therapist
Buddy explains!

The straight part
We know that "Getting to the end of this exhausts one’s patience" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case getting to the end of this exhausts one’s patience = tether.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does TETHER mean?
TETHER noun- A rope, cable etc. that holds something in place whilst allowing some movement
- A strong rope or line that connects a sailor's safety harness to the boat's jackstay
- (by extension) the limit of one's abilities, resources etc.
- The cardinal number three in an old counting system used in Teesdale and Swaledale. (Variant of tethera)
- To restrict something with a tether.
- To connect a cellular smartphone to another personal computer in order to give it access to a hotspot.