Clarke birdied the eighth hole just before play was halted due to inclement weather at 12:05 p.m. local time. He is through 62 holes at 6 under par, with a group of three players tailing him at minus-4.
Officials hope to re-start the final round Monday morning beginning at 9:15 a.m. local time -- 4:15 a.m. (ET).
The tournament has been plagued by weather problems since Thursday, and more rain is expected in the area Monday.
Paul Casey, one of three overnight leaders, is 1 over through seven holes and sits at 4 under. He is joined there by Ross Fisher and Peter Hedblom, who are both even-par through eight holes in their final round.
The other overnight leaders -- Thomas Bjorn and Anthony Wall -- are one shot further back at minus-3 after giving up two shots over seven holes on Sunday.
Just three players in a remaining field of 72 were able to complete their rounds before the stoppage. Damien McGrane and Colm Moriarty shot matching 1-over 73s and hold the clubhouse lead at 3-over-par 291.
Because bad weather was expected Sunday, start times were moved up and players teed off in threesomes off split tees. If the tournament is not finished Monday, the Irish Open will become the second weather-shortened event of the season.
Clarke has played his last 34 holes bogey-free since dropping a stroke on his 11th hole during the second round. The 11-time European Tour winner opened his final round with a birdie at the par-4 first, rattled off six consecutive pars, then birdied the par-5 eighth to take his two-shot lead.