Items from the tool belt are not listed unless they do not work or are not automatically added.Priest gown top and bottom (can be obtained during the quest for 10 coins)
Exit West Ardougne with the help of Kilron or by going through the sewers.
Talk to Elena.
Samples
Note: Do NOT attempt to use any means of teleportation at all while holding the Plague sample! It will disintegrate. The other samples aren't that delicate. You can teleport with those.
Go to Rimmington. To do this quickly you can bank the plague sample and use your Clan vexillum if you have one to teleport to the Clan Camp (any other teleport method with a nearby target location works too), then retrieve the sample from the closest bank. (You can only talk with the Chemist about touch paper if you have the Plague sample with you.) Find the Chemist in the Westernmost house and tell him that Elena needs touch paper. Do not mention the plague sample.
Ask him if he has ideas on how to get the samples past the Varrock guards.