Here is an account from Chapter 16, (The Day of Atonement), of "THE TEMPLE - ITS MINISTRY AND SERVICE", (Alfred Edersheim), which goes into some detail about the duties if the chief priest in the great day. There is another account I am aware of but cannot remember where it comes from, (perhaps Josephus?), where it was said that the most difficult duty of the chief priest in this day was carrying the incense and the censer into the Most Holy place because he actually had to have two hands, (plural), full of incense and therefore was required to carry the censer under his armpit into the Most Holy place, (a task so difficult that the potential fill-ins and those who might be chief priest one day had to rigorously train for this duty). However when I went back to this account it was not the one I thought it was, but it makes the point concerning the censer clear enough, for it states that the one used in the great day, (Yom Kippurim), was larger and therefore different from a regular censer.
THE TEMPLE - ITS MINISTRY AND SERVICE, excerpt Ch. 16 (Alfred Edersheim)
The Confession of Sin and the Sacrifice
With this presentation of the scape-goat before the people commenced the third and most solemn part of the expiatory services of the day. The high-priest now once more returned towards the sanctuary, and a second time laid his two hands on the bullock, which still stood between the porch and the altar, to confess over him, not only as before, his own and his household's sins, but also those of the priesthood. The formula used was precisely the same as before, with the addition of the words, 'the seed of Aaron, Thy holy people,' both in the confession and in the petition for atonement. Then the high-priest killed the bullock, caught up his blood in a vessel, and gave it to an attendant to keep it stirring, lest it should coagulate. Advancing to the altar of burnt-offering, he next filled the censer with burning coals, and then ranged a handful of frankincense in the dish destined to hold it. Ordinarily, everything brought in actual ministry unto God must be carried in the right hand- the incense in the right and the censer in the left. But on this occasion, as the censer for the Day of Atonement was larger and heavier than usual, the high-priest was allowed to reverse the common order. Every eye was strained towards the sanctuary as, slowly bearing the censer and the incense, the figure of the white-robed high-priest was seen to disappear within the Holy Place. After that nothing further could be seen of his movements.
The Mercy-seat
The curtain of the Most Holy Place was folded back, and the high-priest stood alone and separated from all the people in the awful gloom of the Holiest of All, only lit up by the red glow of the coals in the priest's censer. In the first Temple the ark of God had stood there with the 'mercy-seat' over-shadowing it; above it, the visible presence of Jehovah in the cloud of the Shechinah, and on either side the outspread wings of the cherubim; and the high-priest had placed the censer between the staves of the ark. But in the Temple of Herod there was neither Shechinah nor ark- was empty; and the high-priest rested his censer on a large stone, called the 'foundation-stone.' He now most carefully emptied the incense into his hand, and threw it on the coals of the censer, as far from himself as possible, and so waited till the smoke had filled the Most Holy Place.
It very well could be that this censer was not kept in the Most Holy place until after the events of 2Chr 26:19, when king Uzziah went into the secondary sanctuary to burn incense with it in his hand. He may have picked it up from inside the secondary sanctuary as it may have been kept by the altar of incense, (we simply do not know because the text never tells us, at least as far as I know). If this is the case then it seems only logical that this very event and this very time would be when and why they began to keep it behind the veil in the Most Holy place. You probably do not need me to expound those passages I quoted from the Septuagint, (they surely speak of the censer and use the same word as I highlighted), for you can get the meaning from pretty much any English translation but especially in that case from the Brenton English translation of the Septuagint, (bible.hub, etc.). I'll post the Brenton:
2 Chronicles 26:19 LXX Brenton English Translation
19 And Ozias was angry, and in his hand was the censer [το θυμιατηριον - G2369 - Heb 9:4] to burn incense in the temple: and when he was angry with the priests, then the leprosy rose up in his forehead before the priests in the house of the Lord, over the altar of incense [επανω του θυσιαστηριου των θυμιαματων].
"το θυμιατηριον" is most definitely "the censer", (not just "a censer"). Moreover what is used here for the altar of incense at the end of the statement is not the same word but the word for an altar, (G2379 θυσιαστηριον).
In the Ezekiel passage there can be no mistaking how the same word is used for censer: but this time it speaks not of "the censer" but the smaller common censers held by the priests and Levites, (showing even more positively that this word was indeed used for both censers and "the censer").
Ezekiel 8:11 LXX
11 και εβδομηκοντα ανδρες εκ των πρεσβυτερων οικου ισραηλ και ιεζονιας ο του σαφαν εν μεσω αυτων ειστηκει προ προσωπου αυτων και εκαστος θυμιατηριον αυτου ειχεν εν τη χειρι και η ατμις του θυμιαματος ανεβαινεν
Ezekiel 8:11 LXX Brenton English Translation
11 And seventy men of the elders of the house of Israel, and Jechonias the son of Saphan stood in their presence in the midst of them, and each one held his censer [G2369 θυμιατηριον - Heb 9:4] in his hand; and the smoke of the incense went up.