How would you try to motivate a team member who is extremely talented yet lacks motivation to continue in the project?

I think you try and uncover what motivates him/her by asking others who know him (supervisor, colleagues, etc). For some it's recognition, for others money or perks. Are they unmotivated on all projects? Or just this one? If it's all projects, they could have personal issues that are affecting their overall performance. If it's just this one, it could be a personality conflict with other team member(s), or they may not believe the project is worthy of their time and efforts, for whatever reason. You may need to do some tactful investigative work to uncover the issue.

A team member may work as an individual contributor or in collaboration with others in team. It may be possible that this team member is not involved in activities he expertise, other team members feel less comfortable and avoid interaction, higher expectations by the management, less involvement in project activities, reprimand of expertise, experience, seniority during 1x1, feeling of being neglected, etc.

Wage hike, recognition, career growth, and work environment, personal issues can also be few reasons.

I see communication gap here. A team needs to be more open, and come up together.

How to motivate? Motivation is something that will not come overnight. Try to understand the pain area. It could be either work related or personal issues.

For work related issues, make the team member comfortable by involving in project activities, asking for opinion, involving in decision making, recognizing during team meeting, fostering the culture of trust, etc.

For personal issues, discuss, and check if the team member requires time off.