The auction should go:

 

N             S

2N           3♣

3♦           3♠

3N           4♠

 

North as 20-21 HCP and a balanced hand so should open 2N.

We know that a 4/4 major fit would play a trick better than a 5/3 fit or a 6/2 fit so you should bid Stayman asking partner if they have a four-card major

3♦ says “I do not have a have four-card major”

Now comes the fun part of this auction.  Bid 3♠ next showing 5+ spades.  By bidding slowly you’ll find out whether or not partner holds three spades or only two.

When Opener rebids 3NT, you know they do not hold three spades.  With three spades they would have bid 4♠ not 3NT and you might have considered slam with a nine-card spade fit.

The shape of your hand is great, but your suit quality in spades is not very good, you only have eight spades between your two hands and your points, when you are thinking of bidding a slam, are on the low side.  (The maximum points between your two hands is 30).

So I would simply bid 4♠ and stay in game.  It’s possible you might make slam.  If the ♠K is in a favorable position the spades break well, but I wouldn’t push the envelope.

Some players would open 2♣ with the North hand and rebid 2NT, deciding that 21 HCPs and a great five-card suit would push their hand to a higher level.  If North decides to open 2♣, I think you would always get to 6in much the same auction.