The Federal Reserve will increase interest rates next week, as many central bankers have been recently hinting, and that's only the beginning, according to Brookings Institution's Aaron Klein, a Treasury staffer during former President Barack Obama's administration.

"The Fed is racing to get to 1.5 percent for the interest rate so that they can get above the next recession and get out in front," Klein said Monday on CNBC's "Squawk Box."

He said the Fed also wants to create "wiggle room" in case policymakers need to cut rates down the road in the event of an economic slowdown.

In a speech Friday, Fed Chair Janet Yellen was rather transparent about the possibility of a rate hike at the central bank's March 14-15 policy meeting.

The fed funds rate, the benchmark overnight lending target, stands at 0.5 percent to 0.75 percent after a quarter-point increase in December, which marked only the second hike in more than a decade. Fed officials at the December meeting indicated three more rate increases in 2017 were likely.

"There were false starts year after year after year," said Klein, an economic studies fellow at Brookings and a former deputy assistant secretary for economic policy at Treasury. "I think people are going to start to get used to regular Fed rate hikes all year, starting now."

But the Fed tightening does come despite "room to run" in the labor market, he said. "There's still slack in employment. And inflation is still edging toward 2 percent but hasn't hit that yet. We've had years below that level."