Declarer should make 9 or 10 tricks.

The Auction

There are a number of ways that East/West should reach 3NT.

East starts with 1♠  intending to rebid NT at the lowest level to show a balanced hand with 15-16 points.

West has a choice of bids - 2NT showing 10-12 points and a balanced hand or 2♣ , the cheapest of their two 4 card suits, showing clubs and 10+ points.

If West bids 2NT, East will bid 3NT as they know they have enough points for game.

However, I prefer the 2♣  bid by West as it allows East more scope in their rebid should they be weak. With a weak hand East will have to pass a 2NT bid by West, but over a 2♣  bid by West, East's rebid might be 2♥  in which case the partnership will play in 2♥  rather than 2NT.

Let's assume West has bid 2♣ , East now has a choice of bids. They can either bid 3NT knowing they have enough points for game or 2NT showing a balanced 15-16 points. 2NT is a more accurate bid as it allows West with a stronger hand decide whether a slam is possible or not (if East always bids 3NT in this situation West can only judge the points range to be 15-19). Don't worry if the subtly escapes you, it will become clearer when we talk about slam bidding.

If East bids 2NT, West MUST bid 3NT.

The Play

South is on lead and should lead ♠ 3 (fourth highest of their longer suit). In NT you are trying to establish tricks in your longest suit.

East (declarer) should take a moment to count their tricks. They have 8 top tricks - 4 in clubs (AKQJ), 3 in diamonds (AKQ) and 1 in hearts (A). They need 1 more trick to make their contract. Where is it going to come from? Look at the spades - a solid sequence of QJT9 - use these to drive out the A & K before cashing any other winners to establish 2 tricks in spades giving you 10 tricks in total. 

It certainly looks like the defence is going to help declarer with the opening lead of a spade. North won with ♠ A but instead of returning a spade as expected switched to ♥ J. Was this an inspired switch?

Declarer cannot allow the defence to take 3 tricks in hearts (with 2 tricks in spades, the contract will not make).

Normally with small hearts in dummy I would hold up the ♥ A for two rounds then lead a spade when I am thrown in, praying the person who held the ♠ K had no more hearts. However, the holding in dummy of T976 is sufficient to stop the defence from winning more than two heart tricks provided the ace captures one of the defence's picture cards. Sure enough declarer covered the ♥ J with ♥ A. Look what happens now. Declarer leads a spade to the ♠ K. South leads a heart to North's ♥ K but North has no hearts to lead to South's ♥ Q. Declarer gets back in and makes their 10 tricks. 

In fact the only way the defence can restrict declarer to 9 tricks is to start with a heart instead of a spade.

Conclusion

Be prepared to lose the lead in order to establish extra tricks.

Don't cash your winners until you have done this. It may set up winners for the opposition.

Finally, take your winners in the correct order. Look at the club suit. You have 4 winners but only if you play them QJAK. If you start with the A then the K you will find yourself throwing the J on the K. If you start with the A you have time to recover. Play small to the Q. Then play J and use the ♦ A (provided you haven't already played it) to get back to cash the K.