My public library has a copy of Destiny Legendary Edition with all the previous expansions. However, when I put the disk in the PS4, the areas still say "Requires Taken King" even though the game I took out is that edition. One option it gives is to use a redeemeable code. If that redeemeable code is somewhere in the game container, where is it?
So the Taken King is by downloaded/accessible through a code that you enter in to the PS Store. Chances are if you got this from a public library the first person who took the game out was the lucky dog who got the code for free, or the library took the code out. Codes are a one time use, so even if it was in there and the code did not work you would be in the same boat. You will only have access to what the disk gives you.