The quest won't trigger. I have entered Novigrad, yet the gwent quest "High Stakes won't start. All other notices trigger certain quests but not this one.

If you have mods installed, uninstall them.
Than use Galaxy to verify/repair your installation.

If this still doesn't work, try talking to the scribe in the Passiflora.

Entering Novigrad does not trigger this quest. You have to either take the quest from a notice board ('High Stakes Gwent Tournament'), or find the scribe who's turning away a potential competitor in the tournament.

Go to the scribe.

Here's what I found out that (probably) triggers the quest: You have to enter the city, go to main square where they burn witches, witness the burning. After that cutscene, you can (probably) trigger the quest.