Liapis was born in Athens to Konstantinos Liapis, a lawyer, and Antigoni Karamanli (1921–2010). His mother was a younger sister of Konstantinos Karamanlis, who was four times prime minister and twice president of Greece. This means that Liapis is a nephew as well as a first cousin to former prime ministers, the latter being Kostas Karamanlis.
In 1977 he was appointed special advisor on communications and public relations matters at the prime minister’s office, whose incumbent was his uncle Konstantinos Karamanlis.
In 1980, upon the election of Konstantinos Karamanlis as President of Greece, he was appointed director of the President's private office. Liapis retained that position until 1985, when Karamanlis' tenure ended.
He was first elected a member of the Greek Parliament in the 1985 general election, when he was returned for the Greater Athens (B) constituency on the New Democracy ticket. He was reelected at every election until the 2007 general election. He kept his seat until 2009, when he announced that he would not contest that year’s snap election.
From December 1992 to October 1993, he was Deputy Minister for Trade.
In March 2004 he was appointed Minister for Transport and Communications.
In September 2007 he was appointed Minister for Culture, a position he held until January 2009.
He is the author of three political books: "For a radical Renewal", "For a New Morality" and "For a Creative Overthrow".
He is fluent in French and English.
He is married with a son and a daughter.
On 17 December 2013, Liapis was arrested in Athens after he was found driving a luxury jeep with bogus number plates, for which he also had no insurance. Police had performed a check on his vehicle after he had failed to halt at a stop sign.
It subsequently emerged that Liapis had handed the real license plates into the tax office in August of that year to avoid an estimated €1,320 in road taxes.
Liapis was immediately fined €780 for driving an uninsured vehicle and other offences. He was due to stand trial on misdemeanour charges on 19 December, but that was postponed until 30 December. If convicted, faces a suspended jail sentence of between six months to five years.
In a statement issued on December 19, New Democracy announced that it had expelled Liapis from the party.
| Minister for Transport and Communications
10 March 2004 – 19 September 2007
| Ministers of Culture and Sport
19 September 2007 – 8 January 2009