Run an animation with delay in swift

Depending on how your animation is implemented, you could use:

UIView.animate(withDuration: 0.3, delay: 5.0, options: [], animations: { 
//Animations
}) { (finished) in
//Perform segue
}

This will apply a delay before the animations run, then run a completion block (where you execute your segue).

EDIT: You updated your question to use CAAnimations, so I don't think this solution will work.

Make use of UIView.animate(withDuration:)'s completion handler. Basic sample below:

func performMyAnimation() {
  UIView.animate(withDuration: {$duration}, 
      animations: { /* Animation Here */ }, 
      completion: { _ in self.performSegue(withIdentifier: "segueIdentifierHere", sender: nil) }
}

Your animation runs in the animations block. Upon completion, you'll then perform the segue to the next screen.

---

Edit: As the question now includes the animation code, using CABasicAnimation, then perhaps this answer for a CAAnimation callback may work for you.

Basically, you need to wrap your CABasicAnimation call with a CATransaction.

CATransaction.begin()
CATransaction.setCompletionBlock({
    self.performSegue(withIdentifier: "segueIdentifierHere", sender: nil)
})
// Your animation here
CATransaction.commit()

If you're looking for a delay which is standard in Swift 3, then it's probably best to use the DispatchQueue API in conjunction with UIView.animate(withDuration:_:).

If for example you wanted to delay a 1.0 second animation by 3 seconds:

let yourDelay = 3
let yourDuration = 1.0
DispatchQueue.main.asyncAfter(deadline: DispatchTime.now() + .seconds(yourDelay), execute: { () -> Void in
    UIView.animate(withDuration: yourDuration, animations: { () -> Void in
        // your animation logic here
    })
})

Let me know if this makes sense to you