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In the earlier films it is said that Jack bartered for the compass from Tia Dalma. However, in the newest film during Salazar's flashback it shows that the captain of his ship is wounded and hands the compass to Jack.

So how did Jack get his compass and why does this feel like a discrepancy in the plot?

We don't know.

There is no official explanation as to why both different events have happened. We can only theorize. As the other answer says, Jack may have won the compass twice, but I disagree (as that would seem to imply he betrayed the compass before, which would have released Salazar before).

From the wiki:

Jack Sparrow's compass was an unusual navigational instrument most notably used by Captain Jack Sparrow, which he bartered from the voodoo mystic Tia Dalma and later inherited from his captain.

We can theorize, however...

A more logical explanation in my opinion, is that he bartered the compass for his captain, not for himself. In other words, the compass was only his after his Captain's death, when he actually inherited it. Previously, he bargained for it in his captain's behalf. It seems to fit quite nicely with the story, leaves some leeway as to why his previous captain wanted it or cursed Salazar with it, and works well with both perspectives of the story.

According to Pirates of the Caribbean: Dead Man's Chest Jack Sparrow got compass from Tia Dalma.

Tia Dalma: The Compass you bartered from me. It cannot lead you to dis?

According to Pirates of the Caribbean: Dead Men Tell No Tales Jack Sparrow got compass from the captain of a ship.

Actually story and screen play has been written by different writers and they have not followed the exact logic, they have written which logic that suits for that particular part in the movie series.

There is nothing much to think about the logic since movie series continues with new stories and of course by taking few links and leads from prequels.

I'm not sure exactly how canon it is but according to the Pirates Wiki page on the Compass:

Jack Sparrow's compass was an unusual navigational instrument most notably used by Captain Jack Sparrow, which he bartered from the voodoo mystic Tia Dalma and later inherited from his captain.

So apparently he bartered it from Tia Dalma, somehow lost it, gave it away, or alternative and then got it back in the flashback scene we see in Dead Men Tell no Tales.

The same page goes on to say:

However, the compass somehow found its way into the hands of the pirate captain of the Wicked Wench, under whom Jack was serving at the time.

So it appears to be unclear how the compass left Jack after he bartered it off of Tia Dalma till it comes back to him again.

Tia Dalma said he bartered it, right? Maybe she gave him the location of the compass in exchange for him trapping Salazar or some other favor. Obviously, this is still speculation, but it would explain why he had to get the compass from the captain, and could still be considered a barter exchange with Tia Dalma.

I think the compass was Jack's tribute to his captain. This would eliminate any contradiction between the two events. Jack barters the compass from Tia Dalma, which at some point ends up as a tribute to his captain, who cherishes the compass as his most valuable property, even incorporating it into his will. The dying captain, then entrusts the compass back to Jack.

When the compass is offered with a purpose (William Turner when tossing dead bodies: At World's End/ Mr. Gibbs: On Stranger Tides...) , taken ( Blackbeard: On Stranger Tides...), it is not considered a betrayal. My point is, offering it as a tribute won't release your darkest fear.