The questions has many "depends" in the answer. If it is simply a loss of elevator or stabilator control, but everything is there, and nothing is jammed, A later certificaion basis (mid '70's or later design plane) will include a procedure for landing without elevator control. This will be a combination of trim and power, but no elevator. providing this procedure satisfies the following certification requirement:
Sec. 23.145
Longitudinal control.
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(e) It must be possible, by using the normal flight and power controls except the primary longitudinal control, to control the descent of the airplane to a zero rate of descent and to an attitude suitable for a controlled landing, without exceptional piloting skill, alertness, or strength, and without exceeding the operational and structural limitations of the airplane.
If a part of the pitch control system is missing or jammed, that is not applicable.
If the plane is certified to the earlier CAR 3 requirement, which predated Part 23, this requirement is not applicable in CAR 3, so the plane may not have a procedure published.
The CAR 3 1Cessna 172N, as an example, does have a procedure published for this. I've tried it, it's not easy. I would suggest that anyone who needed to do this plan to land on a pavement/concrete runway, certainly not grass, so that a poor landing will not result in the plane digging in, and flipping over - you'd rather slide, that roll into a ball.
A mentor of mine told me that he once had to land with no elevator control in a Lake Amphibian. The elevator pushrod had been in bilge water in winter cruise flight, and froze during the flight. He was able to land on the trim only, though Lakes have a different trim, it's not a tab, but rather a separate little elevator, hydraulically controlled. Still not easy to do!