Heavensward class quest

[MistakeNot]

So i finaly dug my way into heavensward content (at level 59) and i'm wondering if I can go straight to my class quest giver or I have to grind it trough the main story line so I can meet the new NPS that gives my CQ ?

Depends on the class/job and the specific quest.
If the NPC you need to talk to is in a place you have access to - then go ahead and talk to them. If the NPC is in some area you do not have access to yet - then you need to follow the MSQ until you do get access to that area.

The very first extra class quest at level 50 will start at same quest giver that you got previous quests from, and lead you to whatever NPC will give the next quest.