The tabernacle should to be empty before the Mass of the Lord’s Supper on Holy Thursday. All remaining Hosts should be consumed by Holy Wednesday (unless if in the Cathedral, the Mass of the Chrism is to take place on Holy Thursday morning – in that case, all the Hosts should be consumed after that Mass), or if it can’t be done, put away in the rectory. The Eucharist is taken away, reminiscent of the Passion and Death our Lord will undergo.
For this reason, perpetual adoration/daily adoration is temporarily suspended from Holy Thursday up until Our Eucharistic and Risen Lord goes back to the tabernacle after the Communion on Easter Vigil. Some parishes repose the B.S. in the Adoration Chapel on Holy Wednesday night, others just after 12pm on Holy Thursday.