Lines 13-24 Summary

Get out the microscope, because we’re going through this poem line-by-line.

'I'll love you till the ocean
Is folded and hung up to dry
And the seven stars go squawking
Like geese about the sky.

The lover continues quantifying his love using some high-flying figurative language. This time, he uses our old salty friend the sea and the starry skies as comparison points.
His descriptions continue to be pretty fantastic. He's going to love her until the oceans dry up. Wow. (Shmoop is assuming a he speaking to a she, but there are no pronouns given so feel free to follow your heart and imagine the speaker as whatever gender floats your boat.) The ocean becomes clean laundry that's been hung out to dry. We have some more mixing here—the natural world (the ocean) becoming part of the human realm (laundry).
Those seven stars that Auden transforms with a simile into squawking geese could be a reference to the biblical seven stars from Revelation. Each star represents an angel from one of the seven churches of early Christianity. If you don't feel like going the biblical route, the seven stars could also refer to the star cluster Pleiades in the constellation Taurus. These stars are often referred to as the Seven Sisters. Anyway you look at it these seven stars have cultural significance (biblical/astrological).
For the lover to say his love will last until these stars (which have been around for millions of years and will likely be around millions more) become as insignificant as squawking geese is, well, significant.

'The years shall run like rabbits,
For in my arms I hold
The Flower of the Ages,
And the first love of the world.'

Time flies (or hops) when your having fun, or when you're hanging out with the Flower of the Ages.
Auden starts this stanza off with another simile. Time scampers away "like rabbits." It's almost as if Time is scared off by the intensity of their love. When he holds her in his arms, Time becomes insignificant—no more powerful than a bunch of scampering bunnies.
On a scale from 1-10, in the eyes if our lover-speaker, she's, like, infinity. The beloved is the most beautiful woman ever. Her beauty is beyond compare, a beauty for the ages. Even her pet name tells us so—he calls her, "Flower of the Ages." Big talk, yes, but this guy is really feeling it, so let's just go with it.
In fact, not only is she one for the ages in terms of her appearance, their love is also beyond compare. The lover-speaker tells us that theirs is, "the first love of the world." All other lovers pale in comparison--Adam and Eve, Romeo and Juliet, Brad and Angelina, they can't hold a candle to the love between these two. Theirs is the first true love the world has ever seen.
Perhaps this is why the speaker thinks their love has the power to stop Time.

But all the clocks in the city
Began to whirr and chime:
'O let not Time deceive you,
You cannot conquer Time.

Our original speaker, we'll call him the poet-speaker, chimes back in at the beginning of this stanza.
His attention is drawn away from the lover's song by the chiming of the clocks around the city.
What follows is the poem's third voice. We'll call this one the clock-speaker. It's the voice of all those clocks.
Talking clocks? Yup, some more personification at work here. Who better to speak on behalf of Time than some clocks?
The clocks lay things down in a pretty no-nonsense kind of way. Basically they are saying, "Look, you might think you've got Time beat with all this love-for-the-ages stuff. You might think that time has scampered off to bother someone else. But the bottom line is, no one beats time. Tick-Tock."