Charl Schwartzel established a new course record with an 8-under 64. The young South African joined Alastair Forsyth in a tie for third place at 8-under-par 136.
Clarke, who captured this event in 2001, played the back side first on the North Course at The Kildare Hotel & Country Club and opened with a birdie at the 10th. He stumbled with a bogey at the 17th but recovered with a five-foot birdie at the par-5 18th to make the turn at minus-6.
The 34-year-old tallied a birdie at the fourth and hit his approach to 18 feet for a birdie at the par-four seventh. At the par-4 ninth, Clarke knocked his second shot inside eight feet and drained the putt for a closing birdie.
'I like this golf course,' Clarke said of the venue that will host the Ryder Cup in 2006. 'It helps that we have played on this course for some time and I think any bit of local knowledge that helps give us an advantage, a fair advantage, can make a huge difference.'
Price also got started on the back nine and like Clarke, he jumped out of the gate with a birdie at the 10th.
The Welshman, who was a teammate of Clarke's on the victorious European squad at last year's Ryder Cup Matches at The Belfry, coasted along until landing his approach on the fringe at the par-4 first.
Price chipped in for birdie and drained a 15-foot putt for a birdie at the par-4 seventh en route to a bogey-free 69.
'I should probably have shot a 73 or something like that but I kept making four, five or six-footers for par which really kept me going,' said Price.
Mark McNulty was on pace for an excellent round and at one point joined Clarke and Price at 9-under par. He started with two birdies over his first three holes and ran off back-to-back birdies from the 10th to reach 8-under.
The 49-year-old then hit a brilliant approach within four feet for a birdie at the par-4 13th but struggled coming home with two bogeys over his last four holes for a round of 69.
McNulty was joined by Andrew Coltart and Eduardo Romero at 7-under-par 137.
Mathias Gronberg fired a 7-under 65 to finish one shot further back at 6-under-par 138 along with Gary Evans and Jarmo Sandelin.
Colin Montgomerie and Angel Cabrera share 11th at 5-under-par 137.
Local favorite Padraig Harrington rolled in a birdie putt from the fringe at the 18th to make the cut on the number at 2-over-par 146.
Defending champion Michael Campbell also qualified for the weekend. The New Zealander carded a second-round 75 to finish in a group at 1-over-par 145.