The 24-year-old is set to start again when Cardiff Blues visit the Kingspan Stadium on Friday, although Best's return is imminent after he helped Ireland retain their Six Nations title in thrilling circumstances.
And with the GUINNESS PRO12 table brilliantly poised ahead of the final five fixtures, Herring admits he is fully prepared to fight for the new No.2 jersey as the semi-finals approach.
"It is pretty tough. Rory is Ireland's number one and always seems to be playing great rugby, but I like to think that I'm able to start pushing him," he told the Belfast Telegraph.
"Over the last couple of years I have really learned a lot from him and the way he plays is the same as the way I want to play.
"I want to keep pushing and we'll see how it goes.
"Obviously whenever Rory comes back he's going to be looking to start and the best that I can do is just play well, put a bit of pressure on him, and hopefully get a bit of time off the bench and a few starts as well.
"I've worked hard and hopefully I've shown that I can add a bit of impact in the last 20-30 minutes of a game."
Ulster currently sit second in a congested GUINNESS PRO12 table, four points adrift of leaders Glasgow Warriors after suffering a 26-22 defeat at Newport Gwent Dragons last time out.
Herring acknowledges improvements must be made from that result, but insists his side are ready for a return against the Blues.
"We're keen to put things right. We let a chance go to put a bit of distance between ourselves and the other teams - we wanted that buffer," he added.
"It was pretty tough, especially last week when we ended up training pretty hard, I think just to take a bit of the frustration out during the contact sessions.
"It is always hard when you have that wait, but we're fired up and ready to go for this one."
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