Hebrews 10:19 is a hinge on which the letter to the Hebrews turns. We see this sort of thing in all of Paul’s letters - Romans for example… he spends the first 11 chapters developing his doctrine, then in Romans 12:1 he turns to application and implication. Typically, you know you’ve come to the hinge verse when you see a, “therefore”.
Throughout the first 10 chapters we see that Christ is a better Priest, a better Sacrifice, a better mediator of a better covenant… then in verse 19 we see a THEREFORE… that’s like saying… so now what? OR what difference does it make. The remainder of the book will be more practical in nature.
Remember up to this point, the writer to the Hebrews is very much concerned that his readers don’t approach their faith casually and drift slowly but surely into unbelief or worse yet that they begin to trust a system void of the Gospel for their salvation.