In a statement on Wednesday, the TRU said "it invites applications for the head 'Ikale Tahi head coach position to commence upon Board approval".
"This is a rare opportunity to be part of the development and success of one of the most talented teams in World Rugby."
Those interested in the role have until the end of February to apply.
The TRU said it wants someone with experience and skills to lead the national team's campaign into the 2024 season and beyond.
The position became vacant following the 2023 Rugby World Cup in France when former coach Toutai Kefu's contract ended.
Tonga recorded three losses - to Ireland, South Africa and Scotland - and one win - over Romania - in France, finishing their campaign with 5 points.
The 'Ikale Tahi will kick start their campaign with the Pacific Nations Cup.
The 2027 Rugby World Cup qualification playoff against Samoa is also in the pipeline.
Tonga is ranked 16th in World Rugby.