Starky's purpose is enigmatic. Two clues are given:
[Fortune Teller] My word! You are fated to make a grave choice. Whatever will be selected will be decided from the actions of those around you.
Also, in the ending "A Career Change...", two members of his race debate their mission while dining:
Well...? What have youu concluded? The creeatures on this planet are rank K... Noo uunique substance can bee deetected in the liquid... Wee must contact the mother ship and beegin our attack at once... Noo, there is noo neeed to rush. Let us waait foor our comrade, who has preeceeeded us, to maake contact. Hee should bee traveling with the loocals of this planet. It will not bee too laate if wee waait until then. Understood... Wee have all the tiime in the world. Noona-Noona...!!! Nani-Nani...!!!
Perhaps Starky's race is an intergalactic force whose primary purpose is to rid the universe of Lavoids? Maybe once a planet has had a Lavoid for too long, as the CT/CC Planet might have had, they simply destroy it unless there are some valuable resources. Finding none on Crono and Serge's world, they deemed it more appropriate to destroy the Lavoid by destroying the planet than to try to eliminate only the parasite and keep those resources for their parent empire. Or something along those lines.
Alternatively, this race could be responsible for engineering the Lavos strain, and are trying to contain their creation (which has presumably run rampant). This theory begs the question: why would Starky's race investigate the Chrono planet is Lavos is already defeated? An answer lies in humanity, who are a product of Lavos's assisted evolution. They could be perceived as an influence of the beast.
Starky is simply a parody of "Grays" and cute Martian appearance of popular culture.
From: Theory (People)