Q:

Can Valyrian Steel weapons be made now?

If I remember correctly, in Game of Thrones Valyrian Steel is made with dragonfire. There are grown Dragons in Westeros, can the technique of forging Valyrian Steel be reproduced? Is this knowledge somewhere, for example the Citadel?

A:

"the secrets of its making had been lost when the Doom came to old Valyria" (Tyrion IV, ASOS)

It's possible Sam has rediscovered some of those secrets from the Citadel - but there's been no mention of that yet.
Although no new Valyrian steel has been made, Tywin Lannister did have the Stark family sword reforged into two smaller swords. Tobho Mott, the smith who did the work, had Gendry as an apprentice. One fan theory is Gendry has returned in the show so that he can rediscover the secrets of Valyrian steel. Of course, right now he seems more interested in fighting.
These are just theories though - there's no-one we know now knows how to new Valyrian steel :)

