General secretary Dennis Clarke spoke about the request Sunday, a day after Thompson revealed his 18-member Cabinet.
Clarke said the reopening of the National Public Library was at the top of the NUPW's agenda since a meeting with the workers was scheduled for the end of the week.
"The union has been onto the library about the situation there . . . but I would hope I would be in a position to get some answers before we have that meeting on Friday at Independence Square at about 9:30 a.m.
"We were not getting any answers . . . [and] we will need to find out what is going on and that is what that meeting is going to be about. We are not going to move until we know what is going on but we are hoping that we won't have to go that far," he said.
Clarke also noted that the new Public Service Bill was also a critical priority which needed to be discussed with the new Prime Minister, as well as his Minister of Health, David Estwick.
"The holders of the portfolio for the Ministry of Health and the Public Service need to sit down urgently with the NUPW. You just had a Public Service Bill passed and there are a number of things that one needs to revisit and therefore there is a need for us to sit and look at that.
"There is a need to also look generally at the entire Public Service because we have serious problems with accommodation," he said.
In addition, the general secretary said there were a few "proposals" the NUPW needed to present to Thompson which could get the Queen Elizabeth Hospital, especially in the Accident & Emergency Department, "workable", as well as talks on maintenance and funding issues for the medical institution.
He said the NUPW would want to sit with Estwick "very very soon" because there were other issues out there pertaining to the polyclinics which needed to be looked at urgently.
"We need a shift in policy and I am sure that once the minister is willing to listen, then he will get a good feel of what was happening before and what we seek is the best way forward, rather than having a dogmatic approach coming from the political end which obviously is going to be met with a strong approach coming from the union," he said.
Last week, Clarke also told the WEEKEND NATION that the Occupational Health and Safety Bill and industrial relations at Grantley Adams International Airport were other issues that needed to be addressed by the Thompson Administration.