something that is very important and must be dealt with before other things

The management did not seem to consider office safety a priority. 管理部门似乎并不认为应优先考虑办公室安全问题。

My first/top priority is to find somewhere to live. 我首先要考虑的是找个地方住。

You have to learn to get your priorities right/straight (= decide which are the most important jobs or problems and deal with them first). 你必须学会先处理最重要的事。

Repairing the plumbing is a priority task (= more important than other jobs). 修好水管是当务之急。

Banks normally give priority to large businesses when deciding on loans (= they deal with them first because they consider them most important). 银行在发放贷款时通常优先考虑大企业。

Official business requirements obviously take/have priority over personal requests (= official business matters will be dealt with first). 公事显然应放在私事之上。