You will need to download the expansion pass from the Xbox store. Providing you use the same xbox account that purchased the expansion pass on the 360 you will not be charged again.
Were you able to download the expansion pass on xbox 1 through the console's game store? The gamertag that purchased/redeemed the expansion pass on 360 should have a license for the same on xbox 1 through the digital upgrade promo, but you will still need to download the small file that represents that license on the new console. If you haven't downloaded anything on the xbox 1 yet, try restoring licenses (sign into the xb1 with the gamertag that purchased the expansions on 360 if you have multiple gamertags): https://www.bungie.net/en/Help/Article/12181 You can find info on the digital upgrade promo here: https://www.bungie.net/en/Help/Article/12122