The 21-year-old New Zealand international hopes to be involved against Cliftonville in the Europa League first qualifying round first leg at Park Hall on Thursday night
And, eager to add to the one international cap he won in 2008, Draper told BBC Radio Shropshire: "I've got to be playing regularly to get into the Kiwi side, so it's important to make a good start."
The forward joined Saints after a successful spell with Basinsgtoke last season, scoring 15 goals.
"I came because of the chance to play in Europe," he went on. "This is a great club to be at and to have the opportunity to play in Europe made my decision very easy."
Draper lived in Somerset until he was 12, when his family moved to Christchurch in New Zealand.
He played in the 2007 Under 20's World Cup and represented his national side at the Beijing Olympics.
The former Canterbury striker has already scored against Cliftonville in a pre-season friendly.
"I scored a nice goal against them so that gives me a lot of confidence. We had a lot of possession against them, I think we've got a good chance," he added.
TNS director of football Mike Davies has one injury concern ahead the tie - defender Steve Evans has been struggling with a hamstring problem.
• Listen to full match commentary of The New Saints against Cliftonville in the first qualifying round of the Europa League, online at bbc.co.uk/shropshire from 1850 GMT on Thursday, June 30.
Photo: Greg Draper on debut for the Saints against Cliftonville.