To find the climber's elevation after descending 260 feet from the peak, we start with the peak's elevation, which is 14,020 feet.
Now, we subtract the 260 feet descent:
\[ 14,020 , \text{ft} - 260 , \text{ft} = 13,760 , \text{ft} \]
The climber's elevation above sea level after meeting the fellow climber is 13,760 ft.