The 30-year-old has made three appearances for Spurs since his deadline day move from West Ham and has already received praise from Redknapp for his application and endeavour.
But Parker knows his place in the side is never guaranteed and is determined to continue to prove he is worthy of a starting berth.
"I knew when I signed for Spurs that it would be difficult and it is. I will have to work hard and prove myself to stay in the team," the midfielder told Daily Star Sunday.
"You always know when you come to a big club that there will be real competition for places and I think that's healthy.
"But I'm up for the challenge and it can only be good for the squad to have such good competition. We're all pushing each other."
He added: "Things have gone really well for me over the last few years. My main target is to keep fit, try to stay in the side and help as much as I can."