Over time, your clothesline might get a bit loose from the weight of your clothes. Each clothesline requires a different method for getting tight again. But in general, you should be able to untie it from the source, pull it taut and retie it.
However, if you have an umbrella clothesline, for example, you’ll need to pull each line a little to evenly distribute the length of the line. Each line should have an even amount of slack before you push the clothesline higher. Repeat this process until the lines are evenly tight.