If you put it on before Shabbat it is fine, otherwise no. If you had wanted to put the broken plat on you could do that even on Shabbat.
We will first discuss the issue of using the broken plate. The Mishna in Shabbat 124b writes: All vessels that may be moved on Shabbat, their shards may be moved along with them, as long as they are suited for some purpose. Shards of a large bowl may be used to cover the mouth of a barrel. Shards of a glass vessel may be used to cover the mouth of a bottle..
Rabbi Yehuda says: As long as they are suited for a purpose similar to their original use. Shards of a large bowl must be suited to pour soup into them, and shards of a glass vessel must be suited to pour oil into them.
The Gemara explains: Rav Yehuda said that Shmuel said: This dispute in the Mishna is only with regard to a case where the vessels broke on Shabbat eve, as this Sage, Rabbi Yehuda, holds that if they are suited for a purpose similar to their original use, yes, it is permitted, and for some other use, no, it is prohibited. And this Sage, the Rabbis, hold: Even if they are suited for some other use, it is also permitted.
But if the vessels broke on Shabbat, everyone agrees they are permitted. The reason for this is since they were designated for Shabbat use and consequently considered prepared at the onset of Shabbat due to their original vessels, it is permitted to move the shards as well.
The Gemara says that the Chachamim in the Mishna are to the opinion that that a broken utensil like a pot lid, is not Muktzeh as long as it is usable for something even if not for the original use. R’ Yehuda argues that only if it is usable as it what it was originally intended for it is not Muktzeh. This is only if it broke on Shabbat but before Shabbat is fine to use according to everyone.
The Shulchan Aruch Orach Chaim 124b rules like the Chachamim: All utensils which broke even on Shabbat are permitted to move as long as they are able to be used for something like a broken plate can cover a barrel and broken glass can cover a bottle. If it is not usable at all then they are forbidden.
The Ri Milunel understood from the Mishna that “All utensils can be moved: that broken utensils which came from non Muktzeh utensils can be used on Shabbat. However if the object was muktzeh before then its pieces are muktzeh even if they are useable for something. Since they came from forbidden utensils. The Magen Avraham (318:19) understand this from the Rambam as well.
So too here since the plate is something which is a permitted utensil so it is permitted to use since you can use it as a pot cover.
Another thing is that when we say that there must be usable for some purpose, even not the original purpose the Prisha writes, is only when we move them so they don’t get damaged. However if we move them out the way or to use them it is permitted even if they’re not technically usable for anything.
The Pri Megadim understands the Rema (308:6) does not seem to agree. He seems to say that if it can’t be used for something similar to its original purpose. He says :. He seems to say that unless the pieces of glass can be used for something else he is not allowed to move them out of the way. Therefore you should be sure the plate is usable for something.
Now we will discuss In regard to using the tiles leftover from your kitchen. The Gemara in Shabbat 124b: follows. Rav Yehuda said that Shmuel said: The Mishna is where the vessels broke on Shabbat, the Rabbis hold it was prepared before Shabbat ,and Rabbi Yehuda holds that it is an item that came into being on Shabbat. Since they were not shards before Shabbat, they are a new entity and are designated. However, if they were broken before Shabbat everyone agrees that it is permitted to move them, since they were prepared before Shabbat…
Rav Yehuda said that Shmuel said: With regard to the clay seal of a jug that was broken, it is permitted to move it on Shabbat. That was also taught in a Baraita: With regard to the clay seal that was broken, it is permitted to move it, and its shards are permitted to be carried on Shabbat. And one may not break a shard from it to cover a vessel with it or to support the legs of a bed with it. And if one threw it into the garbage dump, it is prohibited to move it because he set it aside from his consciousness.
Rav Pappa strongly objects to this: If that is so, if one throws his cloak into the garbage dump, would you also say that it is prohibited to move it because it is set-aside? Isn’t the cloak still fit for use, and its status is not dependent on his intention? Rather, Rav Pappa said:
If one threw the clay seal of a jug into the garbage dump while it is still day, before Shabbat, it is prohibited to move it on Shabbat because he indicated that he set it aside from use.
Tosfot asks even after the answer of Rav Pappa one may ask that if one throws his shirt away on Erev Shabbat one may not use it?
They answer there is a difference between a lid to a piece of clothing. A lid’s only purpose is to cover the barrel which is broken and since its broken they threw it out and the lid was not designated to cover anything else and that makes it Muktzeh. A shirt which was thrown out on Erev Shabbat is a shirt and ready to be worn . Throwing it in the garbage dos not takeaway the fact that it is a usable utensil.
Therefore something which was thrown away before Shabbat can become Muktzeh unless it was full utensil. So rules the Shulchan Aruch Orach Chaim 308:7.
Therefore in our situation be sure you did not take the it from the garbage. However if you use the tile before Shabbat to cover it , even thought it might be muktzeh, you may designate it to use for your pot. You may even move it around take it off an put it back The is argument whether one needs to designate for all the time or for just one Shabbat the Shulchan Aruch 08 22 rule: You should put it aside to use as a pot cover for the time being.