Sharp questions should be put to the Carter administration at the NATO summit meeting here this week. But allied leaders will hold their tongues rather than embarrass the president on his home turf.

So a NATO meeting that ought to engage attention on serious subjects will turn out, as usual, to be quite dull. Once again, it will be hard to resist the conclusion that the European allies really don't care about their own defense.

The most serious questions have to do with the will of the Carter administration to stand up to a new burst of Soviet assertiveness. The United States is not matching the Russian arms buildup. This country has no formula for meeting Soviet aggrandizement in Africa.

A coup in Afghanistan, which increasing looks to be pro-Soviet and which puts at hazard both Iran and Pakstian, is virtually overlooked in Washington. Nor, though the Carter administration championed human rights with a vengeance, does Washington have any response to the harsh sentence meted out to Soviet dissident Yuri Orlov. So the allies ought to be concerned about whether the Carter administration is truly prepared to face up the huge increase in Soviet power - the development of a capacity to launch a surprise attack on Western Europe itself.

Apart from the questions of standing up, there is the vaguer question of steadiness - of willingness to block out a line and stick to it. A good example is the neutron warhead.

Carter, for reasons still not clear, made a big deal about public coming out for the weapon. He then left the issue of deployment up to a request from the European allies - a stand inconsistent with the notion that the weapon was all that important. Several German leaders and some lesser fry undertook to promote deployment of the weapon. Then, after they were out on a limb, Carter unilaterally decided that he would not deploy it.

Finally, there is the specific question of Turkey. The Turks have refused to accept the proposal made by Carter at the NATO summit meeting at Brussels last year for a long-term commitment to an annual 3 percent increase in defense spending. They have insisted that, before signing on to that commitment, the embargo on military assistance to Turkey should be lifted. The embargo was pushed through Congress by the Greek lobby at the time of the last blowup on Cyprus.

Virtually, all the allies support the Turkish position. The Carter administration also sees the wisdom of lifting the embargo. But it has not gone to the mat on the issue with Congress.

Privately the most weighty allied leaders have no inhibitions about criticizing Carter and his polices and their many changes. But a variet of reasons are working to keep them mute in Washington. French President Valery Giscard d'Estaing does not want to be overly associated with NATO in public. A close connection only deals cards to his Gaullist critics at home. So he sneaked into town for a quick session with Carter Friday and got out before the summit began.

West German Chancellor Helmut Schmidt has been Carter's most vociferous critic, particularly on such matters as human rights and the neutron warhead. But he has learned that he was to live with Carter, and that public disputes don't do him any good. So he has resolved to hold his tongue. Only if provoked is he going to say what he truly believes.

Prime Minister James Callaghan has followed the tradition set by Harold Wislon of going one-up on Britain's European allies by taking the inside track in supporting any and all actions of every American president. He needs the American connection especially now because, otherwise, Britain would be high and dry in Africa. The more so as a general election is in the offing.

Among other countries, only the Turks have a live grievance. But it affects budgetary commitments that stretch over the next decade. The issue can - and probably will - wait until some future meeting.

Mum, in short, is the word of the NATO summit. It seems the Europeans have long since ceased to care seriously about defense. They believe that the combination of NATO ground forces plus the American nuclear threat is enough to deter the Russians. They are probably right.

But they are not all that complacent on economic matters. So unless the Carter administration shapes up on energy and on anti-inflationary police, the next encounter with the allies - at the economic summit in Bonn during mid-July - will be a hardball affair.