"拥立国王者" can be translated into English as "those who installed or enthroned the king" or more concisely as "the king's installers/enthroners" (though the latter is less common in natural usage).
A more common and natural way to express this idea in English might be:
"those who elevated or crowned the king"
"the supporters or backers who brought the king to power"
"the individuals or faction that installed the king"
For a more literal and concise translation, "those who installed the king" would be a good choice. It conveys the meaning of actively participating in or being responsible for the king's ascent to the throne.