If a work is of higher priority for you than another team member how will your team handle apportioning the work?

As per your role and responsibility if a work is higher priority for you than others then you have to clearify your team fellows the importance of the work for the profitability of the company as end of the day all it matters is company's goals and not personal goals. The top employees always prefer their company's goals.

In this given scenario definitely you should take accountability as per your involvement in the priority work assigned for you and think strategically to take an appropriate decision . And also you are being team leader you always consider your sub ordinates consensuses to reach to fruitful conclusion to achieve objective of your priority work.

If your team member is a successful employee and a good team player, he/she should understand priority and what comes first. Both of you are responsible to make sure that tasks are done accurately on time !

Prioritization of work is not by individuals choice, but by the need for the company as a whole in terms of profitability and growth. At whichever level you are positioned, even if you are the CEO. It is imperative to ensure that personal objectives and goals do not cloud your focus. If you are caught in such a bind, where even a senior colleague is unwilling to see the larger picture whilst prioritizing work, you must work towards bringing him/her on board by highlighting the ramifications of the delay to the progress and profitability of the company objectively and also along with the rest of the team members, so you do not stand alone in the quest for success of the company and the individual in question will for sure see reason.

Agree with the previous answers.