Vince, 25, has been named in England's squad for the first Test at Lord's from Thursday and is keen to build on his opening three Tests against Sri Lanka.
He scored just 54 runs in four innings and is keen to contribute more to the top order.
"Whenever you play for England, I think you're under pressure to do well," Vince told BBC Radio Solent.
"Runs are important as that's what keeps you in the team," the right-hander added.
"Hopefully this is a time I can go in and stamp my authority on a place and get some runs."
Vince followed up scores of 51 and 16 in the fifth one-day international and only Twenty20 match against Sri Lanka with 62 for his county against Essex in the T20 Blast on Friday.
With a recall for Yorkshire's Gary Ballance in the top order, Vince is unsure if he will be moved from the number five spot he has occupied so far this summer.
He said: "I'm assuming I'm still at five - but if there's a change, I'll find out when we meet up this week."
Hampshire captain James Vince hopes to "stamp his authority" on his place in the England Test side against Pakistan.